Measuring system for a medium flowing in a process line

ABSTRACT

A measuring system serves for measuring a density of a medium flowing in a process line along a flow axis of the measuring system in the case of a medium which is variable as regards a thermodynamic state, especially a medium which is, at least in part, compressible. The measuring system includes at least one temperature sensor placed at a temperature measuring point, reacting primarily to a local temperature, θ, of medium flowing past, and delivering at least one temperature measurement signal influenced by the local temperature of the medium to be measured; at least one pressure sensor placed at a pressure measuring point, reacting primarily to a local, especially a static, pressure, p, of medium flowing past, and delivering at least one pressure measurement signal influenced by the local pressure, p, in the medium to be measured; as well as a measuring electronics communicating, in each case, at least at times, with the temperature sensor and the pressure sensor. The measuring electronics produces, at least at times, with application both of the temperature measurement signal as well as also at least the pressure measurement signal, as well as with application of at least one numerical compensation factor, especially a digitally stored compensation factor, at least at times, at least one density measured-value, especially a digital, density measured-value, representing, instantaneously, a local density, ρ, which the flowing medium has at a virtual density measuring point, especially a virtual density measuring point predeterminably spaced from the pressure measuring point and/or from the temperature measuring point, along the flow axis. The compensation factor (K) corresponds with a locational variability of at least one thermodynamic variable of the medium, especially a temperature, a pressure or a density, occurring along the flow axis of the measuring system, especially as ascertained in advance and/or during operation, and/or corresponds with a locational variability of the Reynolds number of the flowing medium along the flow axis of the measuring system, especially as ascertained in advance and/or during operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a nonprovisional application based on the followingU.S. provisional applications: U.S. provisional application No.60/929,532, filed on Jul. 2, 2007; U.S. provisional application60/929,529, filed on Jul. 2, 2007; on U.S. provisional application60/929,530, filed on Jul. 2, 2007; and on U.S. provisional application60/929,531, filed on Jul. 2, 2007; and priority is also claimed on thefollowing German applications: on German application 10 2007 030 700.6filed on Jun. 30, 2007; on German application 10 2007 030 690.5, filedon Jun. 30, 2007; on German application 10 2007 030 699.9 filed on Jun.30, 2007; and on German application 10 2007 030 691.3 filed on Jun. 30,2007.

BACKGROUND DISCUSSION

The invention relates to a measuring system for measuring a density of amedium variable with respect to a thermodynamic state, especially atleast partly compressible, flowing in a process line, such as a processpipeline or tube, along a flow axis of the measuring system. Themeasuring system measures by means of a temperature sensor, a pressuresensor and a measuring electronics communicating, in each case, at leastat times, with the temperature sensor and the pressure sensor, andproducing, at least at times, at least one density measured-valuerepresenting, as accurately as possible, a local density of the flowingmedium.

For registering process-describing, measured variables of flowing media,such as the thermodynamic state variable, density, or measured variablesderived therefrom, and for producing measured-values correspondinglyrepresenting such measured variables, industrial process measurementstechnology applies measuring systems installed near to the process. Thisis done especially also in connection with the automation of chemicalprocesses or processes involving adding value to materials. Thesemeasuring systems are often composed of two or more, discrete,measuring, field devices, which communicate with one another and areeach arranged directly at, on or in a process line, through which themedium flows. The measured variables to be registered can include,besides density, for example also other thermodynamic state variables,especially such variables as are registerable by sensor and, as aresult, directly measurable, such as e.g. pressure or temperature,directly or indirectly measurable flow parameters, such as e.g. a flowvelocity, a volume flow, e.g. a volume flow rate, or a mass flow, e.g. amass flow rate, or other complex transport variables, such as e.g. aheat flux, as well as also other measured variables specific to themedium, such as e.g. a viscosity, of an at least partly liquid, powderedor gaseous medium conveyed in a process line embodied, for example, inthe form of a pipeline.

Especially for the indirect (in the following, thus, also referred to asvirtual) measurement of density, based on pressure and temperaturemeasurement signals generated by means of corresponding sensors, as wellas also measured variables possibly derived therefrom, for example massflow or volume flow, a large number of industrial standards have becomeestablished, which recommend a largely standardized, and, thus,comparable, calculation, especially also with application of directlyregistered and, thus, actually measured temperatures and/or pressures,and which find application as a function of application area and medium.Examples of such standards include, by way of example, the industrialstandard “IAWPS Industrial Formulation 1997 for the ThermodynamicProperties of Water and Steam”, International Association for theProperties of Water and Steam (IAWPS-IF97), “A.G.A. Manual for theDetermination of Supercompressibility Factors for Natural Gas—PARResearch Project NX-19”, American Gas Association (AGA-NX19, Library ofCongress No. 63-23358), the international standard ISO 12213:2006, Part1-3 “Natural gas—Calculation of compression factor”, as well as also thetherein cited A.G.A. Compressibility Factors for Natural Gas and OtherRelated Hydrocarbon Gases”, American Gas Association TransmissionMeasurement Committee Report No. 8 (AGA-8) and “High AccuracyCompressibility Factor Calculation for Natural Gases and SimilarMixtures by Use of a Truncated Viral Equation”, GERG Technical MonographTM2 1998 & Fortschritt-Berichte VDI (Progress Reports of the Associationof German Engineers), Series 6, No. 231 1989 (SGERG-88).

Often, the ascertaining of density can also serve for converting adirectly measured, mass flow into an, as a result, indirectly orvirtually measured, volume flow, or vice versa. For direct measurementof flow parameters serving as primary measured variables therefor—thus,for example, a local flow velocity, a local volume flow, or a local massflow—measuring systems of the type being discussed include at least onecorresponding flow sensor, which, by reacting at least predominantly toa flow parameter primarily to be registered for the flowing medium, oralso to changes of the same, delivers, during operation, at least onemeasurement signal, especially an electrical measurement signal,correspondingly influenced by the measured variable primarily to beregistered and representing such as accurately as possible. The at leastone flow sensor can, in such case, be embodied to contact the medium, atleast partially, for example by being immersed therein, or to measureexternally through the wall of the process line or a membrane, ordiaphragm. Usually, the flow sensor is provided, in such case, by meansof a, most often, very complex flow transducer, which is insertedappropriately directly into the process line, or into a bypass,conveying the medium.

Marketed flow transducers are usually implemented as prefabricated,pre-calibrated units equipped with a carrier tube insertable into thecourse of the pertinent process line and also with at least onephysical-to-electrical converting element appropriately pre-assembledtherewith. This converting element, possibly in conjunction with thecarrier tube itself and/or other components of the flow transducer,especially passive-invasive components, such as e.g. flow obstaclesprotruding into the flow and/or active components of the flowtransducer, such as e.g. a coil arrangement placed externally on thesupport tube for generating a magnetic field, or sound producing units,forms the at least one flow sensor delivering the measurement signal.Widely distributed in industrial measurements technology are,especially, magneto-inductive flow transducers, flow transducersevaluating the travel time of ultrasonic waves coupled into flowingmedia, eddy flow transducers, especially vortex flow transducers, flowtransducers with oscillating measuring tubes, flow transducers makinguse of pressure differences, or thermal flow-measuring transducers.Principles of construction and functioning of magneto-inductive flowtransducers are described e.g. in EP-A 1 039 269, U.S. Pat. No.6,031,740, U.S. Pat. No. 5,540,103, U.S. Pat. No. 5,351,554, U.S. Pat.No. 4,563,904, while such for ultrasonic flow transducers appear e.g. inU.S. Pat. No. 6,397,683, U.S. Pat. No. 6,330,831, U.S. Pat. No.6,293,156, U.S. Pat. No. 6,189,389, U.S. Pat. No. 5,531,124, U.S. Pat.No. 5,463,905, U.S. Pat. No. 5,131,279, U.S. Pat. No. 4,787,252. Sincealso the others of the aforementioned principles of measurement usuallyput into practice in industrial flow measuring transducers are likewisesufficiently known to those skilled in the art, a further explanation ofthese and other principles of measurement established in industrialmeasurements technology and implemented by means of flow measuringtransducers can be omitted here.

Industrial measuring systems registering flow parameters involve, often,those, in the case of which, at least one of the measuring pointsdelivering the actual measurement signals and thus, in the following,referred to as real, is formed by means of a compact inline measuringdevice having a flow transducer of the aforementioned kind. Furtherexamples for such measuring systems, especially measuring systems formedby means of compact, inline measuring devices with flow transducersknown per se to those skilled in the art, are presented, additionally,in detail in, among others, EP-A 605 944, EP-A 984 248, EP-A 1 767 908,GB-A 21 42 725, U.S. Pat. No. 4,308,754, U.S. Pat. No. 4,420,983, U.S.Pat. No. 4,468,971, U.S. Pat. No. 4,524,610, U.S. Pat. No. 4,716,770,U.S. Pat. No. 4,768,384, U.S. Pat. No. 5,052,229, U.S. Pat. No.5,052,230, U.S. Pat. No. 5,131,279, U.S. Pat. No. 5,231,884, U.S. Pat.No. 5,359,881, U.S. Pat. No. 5,458,005, U.S. Pat. No. 5,469,748, U.S.Pat. No. 5,687,100, U.S. Pat. No. 5,796,011, U.S. Pat. No. 5,808,209,U.S. Pat. No. 6,003,384, U.S. Pat. No. 6,053,054, U.S. Pat. No.6,006,609, U.S. Pat. No. 6,352,000, U.S. Pat. No. 6,397,683, U.S. Pat.No. 6,513,393, U.S. Pat. No. 6,644,132, U.S. Pat. No. 6,651,513, U.S.Pat. No. 6,651,512, U.S. Pat. No. 6,880,410, U.S. Pat. No. 6,910,387,U.S. Pat. No. 6,938,496, U.S. Pat. No. 6,988,418, U.S. Pat. No.7,007,556, U.S. Pat. No. 7,010,366, US-A 2002/0096208, US-A2004/0255695, US-A 2005/0092101, US-A 2006/0266127, WO-A 88/02 476, WO-A88/02 853, WO-A 95/08758, WO-A 95/16 897, WO-A 97/25595, WO-A 97/46851,WO-A 98/43051, WO-A 00/36 379, WO-A 00/14 485, WO-A 01/02816, WO-A02/086 426, WO-A 04/023081 or WO-A 04/081500, WO-A 05/095902, as well asalso in the not pre-published applications DE 102006034296.8 and102006047815.0 of the assignee.

For the further processing or evaluation of measurement signals producedin the measuring systems, such additionally include at least onecorresponding measuring electronics. The measuring electronics,communicating in suitable manner with the pertinent measuringtransducer, especially also with the at least one converting element,produces during operation, with application of the at least onemeasurement signal, repeatedly, at least one measured-valueinstantaneously representing the measured variable, thus, for example, amass flow measured-value, volume flow measured-value, a densitymeasured-value, a viscosity measured-value, a pressure measured-value, atemperature measured-value, or the like. The measured-values, especiallythe indirectly, or also virtually, measured, density measured-value,are, in such case, often ascertained by means of highly complexcalculations according to one of the mentioned industry standards, forexample “AGA 4”, “AGA 8”, “AGA-NX19, “IAWPS-IF97”, “SGERG-88”, or thelike.

For accommodating the measuring electronics, such measuring systemsinclude, most often, a corresponding electronics housing, which, asproposed e.g. in U.S. Pat. No. 6,397,683 or WO-A 00/36 379, can bearranged remotely from the measuring transducer and connected with suchvia a flexible cable. Alternatively thereto or in supplementationthereof, the electronics housing can, however, also, as shown, forexample, in EP-A 903 651 or EP-A 1 008 836, be arranged directly on themeasuring transducer or on a measuring transducer housing separatelyhousing the measuring transducer, in order to form a compact, inlinemeasuring device, for example a Coriolis mass flow/density measuringdevice, an ultrasonic flow-measuring device, a vortex flow-measuringdevice, a thermal flow-measuring device, a magneto-inductiveflow-measuring device, or the like. In the case in which the electronicshousing is arranged on a measuring transducer housing, the electronicshousing serves, as shown, for example, in EP-A 984 248, U.S. Pat. No.4,716,770 or U.S. Pat. No. 6,352,000, often also for accommodating somemechanical components of the measuring transducer, such as e.g. elementsdeforming during operation on the basis of mechanical effects, elementssuch as membrane, rod, sleeve or tubular deformation- orvibration-elements; compare, in this connection, also the U.S. Pat. No.6,352,000 mentioned above.

In the case of measuring systems of the described kind, the measuringelectronics is usually electrically connected via electrical lines,and/or wirelessly by radio, with a superordinated, electronic, dataprocessing system arranged, most often, spatially remotely, and alsospatially distributed, from the measuring electronics. To this dataprocessing system are forwarded, in near-time, the measured-valuesproduced by the measuring system. The measured-values are forwarded bymeans of measured-value signals carrying the measured-values. Measuringsystems of the described kind are, additionally, usually, by means of adata transmission network (wired- and/or radio-based) provided withinthe superordinated data processing system, connected together and/orwith corresponding electronic process controls, for example programmablelogic controllers (PLCs) installed on-site or process control computersinstalled in a remote control room, where the measured-values producedby means of the measuring system and digitized in suitable manner andcorrespondingly encoded are sent. By means of process control computers,with application of correspondingly installed software components, thetransmitted measured-values can be further processed and visualized ascorresponding measurement results e.g. on monitors and/or converted intocontrol signals for other field devices, such as e.g. magneticallyoperated valves, electric motors, etc., embodied as actuators forprocess control. Accordingly, the data processing system serves usuallyalso for conditioning the measured-value signal delivered from themeasuring electronics corresponding to the requirements of downstreamdata transmission networks, for example suitably digitizing such and, onoccasion, converting it into a corresponding telegram, and/or evaluatingit on-site. For such purposes, provided in these data processingsystems, electrically coupled with the pertinent connection lines, areevaluating circuits, which pre- or further-process, and, if required,suitably convert, measured-values received from the measuringelectronics. Serving for data transmission in such industrial dataprocessing systems, as least sectionally, are, especially serial,fieldbuses, such as e.g. FOUNDATION FIELDBUS, CAN, CAN-OPEN, RACKBUS-RS485, PROFIBUS, etc. or, for example, also networks based on the ETHERNETstandard, as well as the corresponding standardized transmissionprotocols, which are, most often, independent of application.

Usually, it is possible to implement by means of control computers,besides such process visualization, monitoring and control, also remoteservicing, parametering and/or monitoring of the connected measuringsystem. Accordingly, measuring electronics of modern, measuring, fielddevices permit, besides actual measured-value transmission, alsotransmission of various setting- and/or operating-parameters used in themeasuring system, such as e.g. calibration data, measured-value rangesand/or also diagnostic values ascertained internally in the fielddevices. In support of this, operating data intended for the measuringsystem can, most often, likewise be sent via the aforementioned datatransmission networks, which are, most often, hybrid as regardstransmission physics and/or transmission logic.

Besides the evaluating circuits required for processing and convertingmeasured-values delivered from connected measuring electronics,superordinated data processing systems of the described kind include,most often, also electrical supply circuits serving for supplying theconnected measuring electronics and, as a result, also the pertinentmeasuring system with electrical energy, or power. The supply circuitsprovide for the pertinent measuring device electronics an appropriatesupply voltage, which is, on occasion, fed directly by the connectedfieldbus, and drive the electrical lines connected to the measuringdevice electronics, as well as the electrical currents flowingtherethrough. A supply circuit can, in such case, for example, beassigned to exactly one measuring electronics and accommodated togetherwith the evaluating circuit associated with the particular measuringdevice, for example joined to form a corresponding fieldbus adapter, ina housing common to both, embodied e.g. as a top-hat rail module. It is,however, also quite usual to accommodate such superordinated evaluatingcircuits and supply circuits, in each case, in separate housings, onoccasion spatially removed from one another and to wire themappropriately together via external cables.

In the case of industrial measuring systems of the type being discussedhere, often involved, as a result, are spatially distributed measuringsystems, wherein, in each case, a plurality of measured variables ofequal and/or different type are locally registered by sensors at real,mutually separated measuring points along a flow axis of the measuringsystem defined by the process line. These measured variables are fed tothe common measuring electronics in the form of corresponding,electrical, measurement signals by wire, for example also in theso-called HART®-MULTIDROP-method or also in the so-called burst-modemethod, and/or wirelessly, especially by radio and/or optically, onoccasion also encoded into a digital signal or in a digitallytransmitted telegram. For the case described above, in which such ameasuring system is formed by means of a flow transducer, it is thuspossible, for example in addition to the at least one, practicallydirectly registered, flow parameter serving as primary measuredvariable, for example the volume flow, to ascertain, at least indirectlyand, as a result, to measure, by means of the same measuringelectronics, at least virtually, with application also of other,remotely registered, measured variables, for example, a remote, localtemperature or a remote, local pressure in the medium, also derived,secondary measured variables, such as e.g. a mass flow and/or a density.

Experimental investigations on distributed measuring systems of the typebeing discussed, which, as shown e.g. also in U.S. Pat. No. 6,651,512,ascertain, by means of a directly measured, volume flow and a virtuallymeasured density, a mass flow as an indirectly measured variable, haveshown that, especially also despite application of internally, as wellas externally, ascertained, measured variables proved to be very precisein the measuring ranges usual for the pertinent caliber of the processline, significant errors can arise in the result of a measurementvirtual in the above sense. It is quite possible for these errors to liein the range of about 5% of the actual measured variable or even beyond.This is the case, especially also when ascertaining measured variables,such as e.g. volume flow, temperature or pressure, as intermediate,really measured variables, and/or density as an intermediate variablemeasured virtually according to measuring and calculating methodsrecommended in the aforementioned industrial standards.

Further, comparative investigations have, in such case, additionallyshown that the aforementioned measurement errors can show, among otherthings, a certain dependence on the instantaneous Reynolds number of theflow, as well as also on the instantaneous thermodynamic state of themedium. However, it has also been found, in this connection, that, innumerous industrial applications, especially those involvingcompressible and/or at least 2-phase media, the Reynolds number, or thethermodynamic state of the medium, can be not only chronologically butalso spatially variable to a high degree, especially in the direction ofthe flow axis of the measuring system. Besides applications having atleast partially compressible media, additionally especially alsoapplications show a significant transverse sensitivity to spatialvariances of the Reynolds number, or the thermodynamic state, when themeasurement of at least one of the measured variables occurs at ameasuring point (real or virtual), at which the process line has acaliber deviating at least from one of the measuring points (real orvirtual) to the other. This is e.g. the case in the application of flowconditioners reducing the cross section of the line (such as in the caseof e.g. nozzles serving as so-called reducers), which can findapplication in the inlet region of flow measuring transducers, or alsoin the application of flow conditioners increasing the cross section ofthe line (so-called diffusers) in the outlet region of flow measuringtransducers. Measuring systems with such reducers and/or diffusers aredescribed, for example, in GB-A 21 42 725, U.S. Pat. No. 5,808,209, US-A2005/0092101, U.S. Pat. No. 6,880,410, U.S. Pat. No. 6,644,132, U.S.Pat. No. 6,053,054, U.S. Pat. No. 6,644,132, U.S. Pat. No. 5,052,229 orU.S. Pat. No. 6,513,393 and are used, for example, for improvingaccuracy of measurement of flow measuring transducers. It has, in suchcase, been further ascertained that such transverse sensitivities basedon application of reducers and/or diffusers are significant for caliberratios between about 0.6 and 0.7, while their influence for caliberratios with extreme diameter jumps of smaller than 0.2 are quitenegligible.

Another application area having a significant sensitivity to theaforementioned variances as affecting the desired accuracy ofmeasurement concerns, furthermore, those measuring systems, which areprovided for the flow measurement of heavy gases, such as, perhaps,carbon dioxide or also phosgene, or long-chain carbon compounds having amolecular wa of over 30 g/mol.

The above-described spatial variance of the Reynolds number can, inturn, lead to the fact that practically each of the aforementioned,mutually spaced, real measuring points of the distributed measuringsystem has, during operation, a local Reynolds number deviating, to aconsiderable degree, from the local Reynolds number of each of theother, also-used, measuring points. Equally, also the mentioned varianceof the thermodynamic state would lead to the fact that mutually spaced,measuring points of the distributed measuring system can havethermodynamic states differing from one another. In view of this, thus,each of the measured variables, as measured on a distributed basis,would have to be adjusted according to the particularly associated,local Reynolds number and/or the particularly associated, localthermodynamic state, a task which, in the absence of the informationrequired therefor, namely the, in each case, other, but remotelymeasured, state variables, is not directly possible. If, for example,the density and/or the mass flow, calculated on the basis of themeasured state variables pressure and temperature, would be calculatedwithout taking into consideration the variance of the Reynolds number,or thermodynamic state, an additional measurement error would result,having essentially a quadratic dependence on the flow velocity.Accordingly, for the aforementioned configuration, at flow velocities ofclearly less than 10 m/s, the measuring accuracy of about 0.1% to 0.5%,currently strived for, is practically no longer significant.

SUMMARY OF THE INVENTION

Starting from the above-described disadvantages of measuring systems ofthe described kind, especially those ascertaining a mass flow or avolume flow, an object of the invention is to increase the accuracy ofmeasurement for such secondary measured variables ascertained withapplication of spatially, distributedly registered, thermodynamic statevariables such as pressure and/or temperature.

For achieving the object, the invention resides in a measuring systemfor measuring a density of a medium, which is variable as regards athermodynamic state, especially at least partially compressible, flowingin a process line along a flow axis of the measuring system. Themeasuring system includes therefor: At least one temperature sensorplaced at a temperature measuring point, reacting primarily to a localtemperature, θ, of medium flowing past, and delivering at least onetemperature measurement signal influenced by the local temperature ofthe medium to be measured; at least one pressure sensor placed at apressure measuring point, reacting primarily to a local pressure, p,especially a static pressure, of medium flowing past, and delivering atleast one pressure measurement signal influenced by the local pressure,p, in the medium to be measured; and a measuring electronicscommunicating, in each case, at least at times, with at least thetemperature sensor and the pressure sensor, and producing, at least attimes, with application both of the temperature measurement signal andalso at least the pressure measurement signal, as well as withapplication of at least one numerical compensation factor, especially adigitally stored, numerical compensation factor, at least one densitymeasured-value, especially a digital density measured-valuerepresenting, instantaneously, a local density, ρ, of the flowing mediumat a virtual, density measuring point, especially a virtual, densitymeasuring point, predeterminably spaced from the pressure measuringpoint and/or the temperature measuring point along the flow axis,wherein the compensation factor corresponds with a locationalvariability occurring along the flow axis of the measuring system,especially a locational variability ascertained in advance or duringoperation, of at least one thermodynamic state variable of the medium,especially a temperature, a pressure or a density, and/or with alocational variability occurring along the flow axis of the measuringsystem, especially a locational variability ascertained in advance orduring operation, of the Reynolds number of the flowing medium.

In a first embodiment of the invention, it is provided that the at leastone compensation factor is ascertained taking into consideration themedium actually to be measured, especially its composition and/or itsthermodynamic properties, especially during a calibration of themeasuring system with known, reference medium and/or during start-up ofthe measuring system on-site.

Developing this embodiment of the invention further, it is additionallyprovided that the measuring electronics ascertains a compensationfactor, at least once, during start-up of the measuring system; and/orthe measuring electronics repetitively ascertains the compensationfactor during operation of the measuring system, especially inconjunction with a change of at least one chemical property of themedium to be measured or with a replacement of the same with anothermedium; and/or the measuring electronics ascertains the at least onecompensation factor on the basis of a predetermined, specific heatcapacity, c_(p), of the current medium, especially a heat capacityascertained in dialog with a user and/or externally of the measuringelectronics.

In a second embodiment of the invention, it is provided, that themeasuring electronics includes a data memory storing the at least onecompensation factor, especially a data memory embodied as a table memoryand/or a non-volatile memory. Developing this embodiment of theinvention further, it is additionally provided that the data memorystores a plurality of compensation factors ascertained in advance fordifferent media and/or for different circumstances of installation;and/or the measuring electronics selects the at least one compensationfactor taking into consideration the current medium, as well as thecurrent circumstances of installation, from the plurality ofcompensation factors stored in the data memory.

In a third embodiment of the invention, it is provided that themeasuring electronics includes a data memory, especially a non-volatiledata memory, which stores, at least at times, at least one measuringsystem parameter specifying solely the medium currently to be measured,especially a system parameter such as a specific heat capacity, c_(p),of the medium currently to be measured, a molar mass, n, of the mediumand/or the number, f, of degrees of oscillatory freedom of the atoms, ormolecules, of the medium, as determined by the molecular structure ofthe medium.

In a fourth embodiment of the invention, it is provided that themeasuring electronics ascertains the density measured-value withapplication of the at least one measuring system parameter specifyingsolely the medium currently to be measured.

In a fifth embodiment of the invention, it is provided that themeasuring electronics includes a data memory, especially a non-volatiledata memory, which stores, at least at times, at least one measuringsystem parameter specifying both the medium to be measured by means ofthe measuring system as well as also instantaneous circumstances ofinstallation of the measuring system, wherein the circumstances ofinstallation are determined by the arrangement of pressure-,temperature- and density measuring points relative to one another, aswell as, in each case, by the form and size of the process line in theareas of the pressure-, temperature- and density measuring points. In afurther development of this embodiment of the invention, the measuringelectronics ascertains the density measured-value with application ofthe at least one measuring system parameter specifying both the mediumcurrently to be measured by means of the measuring system as well asalso instantaneous circumstances of installation of the measuringsystem.

In a sixth embodiment of the invention, it is provided that themeasuring electronics includes a data memory, especially a non-volatiledata memory, which stores, at least at times, at least one measuringsystem parameter of a first kind specifying the medium currently to bemeasured, especially a specific heat capacity of the medium currently tobe measured, a molar mass of the medium and/or the number of degrees offreedom of the medium, and which stores, at least at times, at least onemeasuring system parameter of a second kind specifying both the mediumcurrently to be measured as well as also instantaneous circumstances ofinstallation of the measuring system, wherein the instantaneouscircumstances of installation are determined by the arrangement ofpressure-, temperature- and density-measuring points relative to oneanother, as well as, in each case, by the form and size of the processline in the regions of the pressure-, density- and/ortemperature-measuring points, and wherein the measuring electronicsascertains the density measured-value with application at least of themeasuring system parameter of the first kind and the measuring systemparameter of the second kind.

In a seventh embodiment of the invention, it is provided that themeasuring electronics receives, at least at times, numerical parametervalues, especially numerical parameter values ascertained, externally ofthe measuring system and/or near in time, for at least one measuringsystem parameter specifying a medium to be measured and/or instantaneouscircumstances of installation of the measuring system, especially a heatcapacity, c_(p), for medium to be measured, which represents a specificheat capacity, c_(p), earlier ascertained and/or measured remotely fromthe density measuring point for the medium to be measured.

In an eighth embodiment of the invention, it is provided that themeasuring electronics communicates, especially via fieldbus, at least attimes, especially by wire and/or by radio, with a superordinated,electronic, data processing system. In a further development of thisembodiment of the invention, it is additionally provided that themeasuring electronics transmits the density measured-value to the dataprocessing system and/or wherein the measuring electronics receives fromthe data processing system, at least at times, measuring systemparameters specifying numerical parameter values for the medium to bemeasured currently, especially its thermodynamic properties and/or itschemical composition, especially a specific heat capacity, c_(p), of themedium currently to be measured, a molar mass, n, of the currently to bemeasured medium and/or the number, f, of degrees of oscillatory freedomof the atoms, or molecules, of the currently to be measured medium,and/or that the measuring electronics is connected with thesuperordinated, electronic, data processing system by means of afieldbus, especially a serial fieldbus.

In a ninth embodiment of the invention, it is provided that themeasuring electronics ascertains, during operation, at least at times, aspecific heat capacity, c_(p), of the currently to be measured medium,especially on the basis of the formula:

${c_{P} = {\left( {1 + \frac{f}{2}} \right) \cdot \frac{R}{n}}},$

wherein n is a molar mass, R, the absolute gas constant, with R=8.3143J/(K mol) and f, a number, determined by the molecular structure of themedium, of degrees of oscillatory freedom of its atoms, or molecules.

In a tenth embodiment of the invention, it is provided that themeasuring electronics generates, repetitively, a temperaturemeasured-value, especially a digital temperature measured-value, basedon the temperature measurement signal, and wherein the temperaturemeasured-value represents, instantaneously, the temperature of themedium at the temperature measuring point.

In an eleventh embodiment of the invention, it is provided that themeasuring electronics generates, repetitively, a pressuremeasured-value, especially a digital pressure measured-value, based onthe pressure measurement signal, and wherein the pressure measured-valuerepresents a pressure instantaneously reigning in the medium, especiallyat the pressure measuring point.

In a twelfth embodiment of the invention, it is provided that themeasuring system further includes a flow sensor placed at a flowmeasuring point and reacting, primarily, to a local flow parameter,especially a flow parameter averaged over a cross section of the processline, especially a flow velocity, a volume flow or a mass flow, of themedium to be measured, especially also changes of the same, and whereinthe flow sensor delivers at least one flow measurement signal influencedby the local flow parameter.

Developing this embodiment of the invention further, it is provided thatthe measuring electronics communicates, at least at times, also with theflow sensor, and wherein the measuring electronics ascertains thedensity measured-value with application also of the flow measurementsignal; and/or

-   -   the medium has, at the virtual density measuring point, a        thermodynamic state corresponding to a thermodynamic state of        the medium at the velocity measuring point; and/or    -   the virtual density measuring point and the flow measuring point        at least partially overlap one another, especially they are        coincident; and/or    -   the temperature measuring point and the flow measuring point at        least partially overlap one another, especially they are        coincident; and/or    -   the pressure measuring point and the flow measuring point at        least partially overlap one another; and/or    -   the density measured-value represents a local density of the        medium in the region of the flow sensor; and/or    -   the measuring electronics communicates with the flow sensor by        means of a field bus, especially a serial field bus, and/or        wirelessly by radio; and/or    -   the measuring electronics communicates, at least at times, with        the flow sensor, wherein the measuring electronics ascertains,        with application at least of the flow measurement signal, a        velocity measured-value, especially a digital flow        measured-value, which represents instantaneously the flow        velocity of the flowing medium.

In a thirteenth embodiment of the invention, it is provided that themeasuring electronics produces the density measured-value withapplication of at least one density correction value ascertained at runtime, dependent both on a flow velocity of the medium as well as also onthe local temperature reigning at the temperature measuring point,wherein the correction value corresponds with an instantaneous,locational variability of at least one thermodynamic state variable ofthe medium, especially with such an instantaneous, locationalvariability related to the medium currently to be measured as well as toinstantaneous circumstances of installation and/or with such aninstantaneous, locational variability occurring along the flow axis ofthe measuring system, and/or wherein the correction value correspondswith an instantaneous locational variability of the Reynolds number ofthe flowing medium, especially with a locational variability of theReynolds number related to the medium and/or the type of construction ofthe measuring system, or with an instantaneous variability of theReynolds number occurring along the flow axis of the measuring system.

Further developing this embodiment of the invention, it is additionallyprovided that the measuring electronics ascertains, during operation, avelocity measured-value, especially a digital velocity measured-value,representing, instantaneously, the flow velocity of the flowing mediumand that the measuring electronics ascertains, with application of thevelocity measured-value as well as the temperature measured-value, thedensity correction value; and/or

-   -   the measuring electronics compares, repetitively, during        operation, the density correction value with at least one        predetermined reference value; and/or    -   the measuring electronics, based on a comparison of density        correction value and reference value, quantitatively signals an        instantaneous deviation of the density correction value from the        reference value and/or generates an alarm, which signals an        undesired discrepancy, especially an unallowably high        discrepancy, between density correction value and associated        reference value.

In a fourteenth embodiment of the invention, it is provided that themeasuring electronics, based on the pressure measurement signal, as wellas on the temperature measurement signal, ascertains a provisionaldensity measured-value, especially according to one of the industrystandards AGA 8, AGA NX-19, SGERG-88 IAWPS-IF97, ISO 12213:2006,representing a density which the flowing medium only apparently has atthe virtual density measuring point.

Further developing this embodiment of the invention, it is additionallyprovided that the measuring electronics ascertains, repetitively duringoperation, a density error corresponding with a deviation, especially arelative deviation, of the provisional density measured-value from thedensity measured-value, and especially issues such also in the form of anumerical, density measured-value; and/or

-   -   the measuring electronics issues an instantaneous density error        corresponding with a deviation, especially a relative deviation,        of provisional density measured-value and density        measured-value, in the form of a numerical, density error value        and/or compares the instantaneous density error with at least        one predetermined reference value and, based on this comparison,        generates, at times, an alarm signaling an undesired, especially        impermissibly high, discrepancy between provisional density        measured-value and density measured-value.

In a fifteenth embodiment of the invention, it is provided that themeasuring system includes, further, at least one flow sensor placed at aflow measuring point and reacting primarily to a local flow parameter,especially a flow parameter averaged over a cross section of the processline, especially a flow velocity, a volume flow or a mass flow of themedium to be measured, especially also to changes of the same, anddelivering at least one flow measurement signal influenced by the localflow parameter, wherein

-   -   the measuring electronics communicates, at least at times, with        the flow sensor and wherein the measuring electronics, with        application at least of the flow measurement signal, ascertains        a volume flow measured-value, especially a digital volume flow        measured-value, representing, instantaneously, a volume flow        rate of the flowing medium; and/or    -   the measuring electronics ascertains, with application at least        of the density measured-value and the volume flow        measured-value, a mass flow measured-value, especially a digital        mass flow measured-value, representing, instantaneously, a mass        flow rate of the flowing medium; and/or        wherein the measuring electronics ascertains, with application        at least of the temperature measurement signal, the pressure        measurement signal and the flow measurement signal, a mass flow        measured-value, especially a digital mass flow measured-value,        representing, instantaneously, a mass flow rate of the flowing        medium; and/or        the flow measuring point is arranged upstream of the temperature        measuring point and/or upstream of the pressure measuring point;        and/or    -   the at least one flow sensor is formed by means of at least one        piezoelectric element and/or by means of at least one        piezoresistive element; and/or    -   the at least one flow sensor is formed by means at least of an        electrical resistance element, especially a resistance element        through which a heating current flows, at least at times; and/or    -   the at least one flow sensor is formed by means of at least one        measuring electrode tapping electrical potentials, especially a        measuring electrode contacting flowing medium; and/or    -   the at least one flow sensor is formed by means of at least one        measuring capacitor reacting to changes of the flow parameter;        and/or    -   the at least one flow sensor, especially a flow sensor        protruding at least partially into a lumen of the process line,        is located downstream of at least one bluff body immersed in the        medium and protruding into a lumen of the process line.

In a sixteenth embodiment of the invention, it is provided that themeasuring electronics communicates with the temperature sensor by meansof a fieldbus, especially a serial fieldbus, and/or wirelessly by radio.

In a seventeenth embodiment of the invention, it is provided that themeasuring electronics communicates with the pressure sensor by means ofa field bus, especially a serial fieldbus, and/or wirelessly by radio.

In an eighteenth embodiment of the invention, it is provided that themedium at the density measuring point is in a thermodynamic statediffering, at least at times, significantly, especially to a degreesignificant for a desired accuracy of the measuring accuracy of themeasuring system, as regards at least one local, thermodynamic statevariable, especially a temperature and/or a pressure and/or a density,from a thermodynamic state of the medium at the temperature measuringpoint and/or a thermodynamic state of the medium at the pressuremeasuring point.

In a nineteenth embodiment of the invention, it is provided that theflowing medium has a Reynolds number greater than 1000.

In a twentieth embodiment of the invention, it is provided that themedium is compressible, having, especially, a compressibilityK=−1/V·dV/dp, which is greater than 10⁻⁶ bar⁻¹, and/or is at leastpartially gaseous. The medium can, in such case, be a gas loaded withsolid particles and/or with droplets.

In a twenty-first embodiment of the invention, it is provided that themedium has two or more phases. One phase of the medium can, in suchcase, be liquid and/or the medium can be a liquid containing gas and/orsolid particles.

In a twenty-second embodiment of the invention, it is provided that themeasuring system further includes a display element communicating, atleast at times, with the measuring electronics, for visual signalizingat least of the density measured-value.

In a twenty-third embodiment of the invention, it is provided that theprocess line is embodied, at least sectionally, especially in the regionat least of the density measuring point and/or in the region at least ofthe pressure measuring point, as a pipeline essentially stable in format least under operating pressure, especially in the form of a rigidpipeline and/or a pipeline having a circular cross section.

In a twenty-fourth embodiment of the invention, it is provided that theprocess line is embodied at least sectionally, especially in the regionbetween density measuring point and pressure measuring point and/orbetween density measuring point and temperature measuring point, as anessentially straight pipeline, especially a pipeline having a circularcross section.

In a twenty-fifth embodiment of the invention, it is provided that theprocess line has at the virtual density measuring point a caliberdiffering from a caliber of the process line at the pressure measuringpoint. Developing this embodiment of the invention further, it isprovided that the caliber of the process line is greater at the pressuremeasuring point than the caliber of the process line at the virtualdensity measuring point, especially it is provided that a caliber ratioof the caliber of the process line at the pressure measuring point tothe caliber of the process line at the virtual density measuring pointis kept greater than 1.1.

In a twenty-sixth embodiment of the invention, it is provided that acaliber ratio of a caliber of the process line at the pressure measuringpoint to a caliber of the process line at the virtual density measuringpoint is kept smaller than 5.

In a twenty-seventh embodiment of the invention, it is provided that acaliber ratio of a caliber of the process line at the pressure measuringpoint to a caliber of the process line at the virtual density measuringpoint is kept in a range between 1.2 and 3.1.

In a twenty-eighth embodiment of the invention, it is provided that theprocess line has, between the virtual density measuring point and thepressure measuring point, a line segment which is embodied as adiffuser, especially a funnel-shaped diffuser, having a lumen wideningin the flow direction, especially continuously widening.

In a twenty-ninth embodiment of the invention, it is provided that theprocess line has, between the virtual density measuring point and thepressure measuring point, a line segment which is embodied as a nozzle,especially a funnel-shaped nozzle, having a lumen narrowing in the flowdirection, especially continuously narrowing.

In a thirtieth embodiment of the invention, it is provided that theprocess line has at the virtual density measuring point a caliber whichis essentially equal to a caliber of the process line at the pressuremeasuring point.

In a thirty-first embodiment of the invention, it is provided that theprocess line has, at the virtual density measuring point, a caliberdiffering from a caliber of the process line at the temperaturemeasuring point. Developing this embodiment of the invention further, itis additionally provided that the caliber of the process line is greaterat the temperature measuring point than the caliber at the virtualdensity measuring point, especially that a caliber ratio of the caliberof the process line at the temperature measuring point to the caliber ofthe process line at the virtual density measuring point is kept greaterthan 1.1.

In a thirty-second embodiment of the invention, it is provided that acaliber ratio of the caliber of the process line at the temperaturemeasuring point to the caliber of the process line at the virtualdensity measuring point is kept smaller than 5.

In a thirty-third embodiment of the invention, it is provided that acaliber ratio of the caliber of the process line at the temperaturemeasuring point to the caliber of the process line at the virtualdensity measuring point is kept in a range between 1.2 and 3.1.

In a thirty-fourth embodiment of the invention, it is provided that theprocess line has, between the virtual density measuring point and thetemperature measuring point, a line segment embodied as a diffuser,especially a funnel-shaped diffuser, having a lumen widening in the flowdirection, especially continuously widening.

In a thirty-fifth embodiment of the invention, it is provided that theprocess line has, between the virtual density measuring point and thetemperature measuring point, a line segment embodied as a nozzle,especially a funnel-shaped nozzle, having a lumen becoming narrower inthe flow direction, especially continuously narrower.

In a thirty-sixth embodiment of the invention, it is provided that theprocess line has, at the virtual density measuring point, a caliberessentially equal to a caliber of the process line at the temperaturemeasuring point.

In a thirty-seventh embodiment of the invention, it is provided that thevirtual density measuring point is placed upstream of the temperaturemeasuring point and/or upstream of the pressure measuring point.

In a thirty-eighth embodiment of the invention, it is provided that thepressure measuring point is arranged downstream from the temperaturemeasuring point.

In a thirty-ninth embodiment of the invention, it is provided that aseparation of the pressure measuring point from the virtual densitymeasuring point is different from a separation of the temperaturemeasuring point from the virtual density measuring point.

In a fortieth embodiment of the invention, it is provided that aseparation of the pressure measuring point from the virtual densitymeasuring point is greater than a separation of the temperaturemeasuring point from the virtual density measuring point.

In a forty-first embodiment of the invention, it is provided that aseparation of the pressure measuring point from the virtual densitymeasuring point is greater than a caliber of the process line at thepressure measuring point and/or wherein a separation of the pressuremeasuring point from the temperature measuring point is greater than acaliber of the process line at the pressure measuring point.

Developing this embodiment of the invention further, it is additionallyprovided that a separation of the pressure measuring point from thevirtual density measuring point corresponds at least to 3-times,especially more than 5-times, a caliber of the process line at thepressure measuring point and/or that a separation of the pressuremeasuring point from the temperature measuring point corresponds atleast to 3-times, especially more than 5-times, a caliber of the processline at the pressure measuring point.

In a forty-second embodiment of the invention, it is provided that themeasuring electronics includes a microcomputer. Developing thisembodiment of the invention further, it is additionally provided thatthe measuring electronics produces at least the density measured-valueby means of the microcomputer.

In a forty-third embodiment of the invention, it is provided that themeasuring system further includes at least one electronics housing,especially an explosion- and/or pressure- and/or impact- and/orweather-resistant housing, in which the measuring electronics is atleast partially accommodated. In a further development of thisembodiment, it is additionally provided that the at least one,especially metal, electronics housing is held to the process line and/orplaced in the immediate vicinity of the virtual density measuring point.

A basic idea of the invention is to improve accuracy of measurement ofmeasuring systems of the described kind by ascertaining, with improvedaccuracy, the density derived from, indeed, real, but, however, ofnecessity, distributedly measured, state variables. This derived densityserves as a central measured variable in numerous applications ofindustrial measurements technology in the case of flowing media. Theimproved accuracy is achieved by taking into consideration possiblespatial variance, especially also the degree thereof, of Reynolds numberand/or thermodynamic state of the flowing medium. This is done in thecase of the measuring system of the invention by a reliable calculatingof the density, by referencing it to a reference point defined earlierfor the particular measuring system and serving as a locationally fixed,imaginary, measuring point. The density is, thus, measured virtually.Developing this basic idea further, the measurement accuracy, with whichthe measuring system ascertains the local density, can be significantlyimproved further by having the measuring system ascertain said densityalso taking into consideration an equally locally measured, extant flowvelocity, in order to achieve a further compensation of the erroraccompanying the mentioned variances of Reynolds number and/orthermodynamic state of the flowing medium.

The invention is based, in such case, on the surprising discovery thatspatial variance in the Reynolds number and/or in the thermodynamicstate, and the measurement errors associated therewith, can be projectedonto a single dimension lying in the flow direction and/or coincidingwith the flow axis of the measuring system and, thus, can be mapped intoa correspondingly simplified set of measuring system parameters, whichcan be ascertained, at least predominantly in advance, experimentallyand/or with computer support, for example in the course of a calibrationof the measuring system, during completion of manufacturing and/orduring start-up of the same. The spatial variances, or their extent and,as a result, also the set of device parameters, are, it is true,specific for each concrete measuring system and each concrete medium, sothat the calibration is individual, but such can then, however, beviewed as invariant in the face of possible changes of Reynolds numberand/or thermodynamic state arising during operation, if the measuringsystem remains unchanged, with essentially constant medium as regardsits chemical composition. In other words, for a given, distributedmeasuring system, the size of changes of the thermodynamic state arisingalong the flow axis can be determined ahead of time, so that theirinfluence can be calibrated and, as a result, also compensated withaccuracy sufficient for the measurements, with it having been found,surprisingly, that the size of the change is largely constant for agiven measuring system with constant medium, so that such can be mappedinto a set of, it is true, specific, but also constant, deviceparameters.

An advantage of the invention is additionally to be seen in the factthat the fundamental method can be directly retrofitted into numerous,already installed, measuring systems, at least insofar as the measuringdevice electronics permits a change of the pertinent processingsoftware.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, as well as additional advantageous embodiments, will nowbe explained in the following on the basis of examples of embodiments,on occasion with reference to the drawing, the figures of which show asfollows:

FIG. 1 perspectively, in side view, a measuring system for measuring alocal density possessed by a medium flowing in a process line at adensity measuring point, by means of a pressure sensor arranged at apressure measuring point and a temperature sensor arranged at atemperature measuring point;

FIG. 2 the measuring system of FIG. 1, this time in the form of a blockdiagram;

FIGS. 3 a, 3 b perspectively and partially sectioned, in views fromdifferent angles, eddy flow transducer suitable for application in ameasuring system of FIG. 1 and working according to the vortexprinciple; and

FIGS. 4 a to 4 h schematically in section, different variants forembodying the process line and for relative arrangement of theindividual measuring points in the measuring system of FIG. 1.

DETAILED DISCUSSION

FIG. 1 shows, schematically, a measuring system 1, which can bemodularly constructed and which is suitable, and provided, forascertaining, at least at times, and very precisely, and, equally veryrobustly, a density of a medium flowing in a process line 20 and formapping such, occasionally even in real time, into a corresponding,reliable, for example even digital, density measured-value X_(ρ).Besides a single phase medium, it is also possible that the medium canhave two or more phases. Examples of media include e.g. gas, liquid(which can contain gas and/or solid particles), a gas containing solidparticles and/or droplets, vapor or steam (which can be a saturatedvapor or dry steam), or the like, such as hydrogen, nitrogen, chlorine,oxygen, helium or compounds and/or mixtures formed thereof, such as e.g.carbon dioxide, water, phosgene, air, natural gas or other hydrocarbonmixtures.

Especially, the measuring system serves for measuring, very accurately,the density of the flowing medium also for the case in which the mediumis variable as regards a thermodynamic state in the direction along theflow axis of the measuring system, such as can be the case, for example,in situations involving media reacting within the process line or forsectionally cooled media or for sectionally heated media, compressiblemedia and/or in the case of process lines of cross section varying inthe direction of the flow axis. The measuring system is further providedfor ascertaining density of flowing media having a Reynolds number, Re,greater than 1000, and/or compressible media having a compressibility,K, of more than 10⁻⁶ bar⁻¹.

The measuring system includes therefor: At least one temperature sensorplaced at a temperature measuring point M_(θ), primarily reacting to alocal temperature, θ, and delivering at least one temperaturemeasurement signal x_(θ) influenced by such local temperature, of themedium to be measured flowing past; as well as at least one pressuresensor placed at a pressure measuring point M_(p), reacting primarily toa local, e.g. static and/or absolute, pressure, p, of, and delivering atleast one pressure measurement signal x_(p) influenced by such localpressure in, the medium to be measured flowing past. Although thepressure measuring point in the example of an embodiment shown here islocated downstream from the temperature measuring point, it can, in caserequired, of course, also be arranged upstream of the temperaturemeasuring point.

Besides the temperature sensor and pressure sensor, the measuring systemincludes, additionally, at least one measuring electronics 100communicating, at least at times, both with the temperature sensor andwith the pressure sensor and receiving, by wire and or wirelessly,measurement signals x_(θ), x_(p) from the temperature sensor and thepressure sensor. The measurement signals x_(θ), x_(p) can, if required,be appropriately converted before being sent to the measuringelectronics 100.

Serving as temperature sensor can be, for example, an industrialtemperature sensor such as e.g. a thermocouple or a resistancethermometer of type Pt 100 or Pt 1000, while the pressure sensor can be,for example, an industrial, especially absolutely, and/or relatively,measuring, pressure sensor, e.g. one with a capacitive pressuremeasuring cell. Of course, if necessary, also other pressure measuringcells converting pressures registered and transferred from the mediuminto corresponding measurement signals can be used, as well as othersuitable temperature sensors. The temperature sensor can, additionally,be provided, for example, as a component of a self-sufficient,industrial grade, temperature measuring device having its ownmeasuring-device electronics. Such temperature measuring devices, knownper se to those skilled in the art, are well established in industrialprocess measurements technology and are sold, for example, also by thefirm, Endress+Hauser Wetzer GmbH+Co. KG, under the designations“Easytemp TSM” or “Omnigrad T”. Alternatively thereto or insupplementation thereof, the temperature sensor can, as explained inmore detail below, also be embodied as an integral part of a complexin-line measuring device possibly registering even a plurality ofmeasurement variables of the flowing medium. Equally, the pressuresensor also can be an integral part of such a complex, inline, measuringdevice, or a component of a self-sufficient, industrial grade, pressuremeasuring device with its own measuring-device electronics. Suchpressure measuring devices, likewise known to those skilled in the art,are also well established in industrial process measurements technologyand are sold, for example, also by the firm, Endress+Hauser GmbH+Co. KGunder the designations “Cerabar S”, “Cerabar M” or “Cerabar T”. Also,the pressure sensor and the temperature sensor can, however, also beprovided in the form of a single measuring device for pressure andtemperature measurement, for example, an industrial, combination,measuring device as proposed in WO-A 97/48970.

As shown schematically in FIG. 1, the measuring electronics can beaccommodated, at least partly, in an electronics housing 110, especiallyan explosion- and/or pressure- and/or impact- and/or weather-resistanthousing. The electronics housing 110, for example of metal, can, as alsoshown in FIG. 1, on occasion, be mounted on the process line.

For the measurement-system-internal, further processing of the pressuremeasurement signal and the temperature measurement signal, an embodimentof the invention additionally provides in the measuring electronics amicrocomputer μC, which serves especially also for producing the densitymeasured-value X_(ρ), and which can be formed, for example, by means ofat least one microprocessor and/or by means of at least one signalprocessor. Alternatively thereto or in supplementation thereof, forimplementing the microcomputer μC, also application-specific,integrated, ASIC circuits and/or programmable logic components orsystems can be used, such as e.g. so-called FPGAs (field programmablegate array) and/or, as also proposed in WO-A 03/098154, so-called SOPCs(system on programmable chip) can be used. Furthermore, the measuringelectronics includes, in another embodiment of the invention, at leastone display element HMI, for example, placed in the immediate vicinityof the measuring electronics and communicating, at least at times, withthe measuring electronics, especially with the microcomputer possiblyprovided therein, for the visual signaling at least of the densitymeasured-value. Display element HMI can, in such case, be embodied alsoin the form of a combined, display and servicing element, which permits,besides the visualizing of measured-values, also user input of servicecommands parametering, and/or controlling, the measuring electronics.

In a further embodiment of the invention, it is additionally providedthat the measuring electronics generates, based on the temperaturemeasurement signal, for example also with application of the, onoccasion, provided microcomputer, repetitively, a temperaturemeasured-value X_(θ), especially a digital one, instantaneouslyrepresenting a local temperature of the medium, especially thetemperature of the medium at the temperature measuring point, and/orthat the measuring electronics generates, based on the pressuremeasurement signal x_(p), for example, in turn, with application of the,on occasion, provided microcomputer, repetitively, a pressuremeasured-value X_(p), especially a digital one, instantaneouslyrepresenting a pressure reigning in the medium, especially at thepressure measuring point.

At least for the above-described case, in which the measuring system isformed by means of two, or also more, self-sufficient, measuringdevices, in the case of the measuring system of the invention, also themeasuring electronics itself can be implemented by appropriateinterconnecting, by wire and/or wirelessly, of individual measuringdevice electronics thus forming subcomponents of the measuringelectronics and can, as a result, also be built-up modularly. In suchcase, the measuring electronics can communicate with the temperaturesensor and/or with the pressure sensor, for example, by means of afieldbus, especially a serial fieldbus. Alternatively to a distributedconstruction, the measuring electronics can, however, also be embodied,in case necessary, in the form of a single electronics module, intowhich the measurement signals produced by the pressure and/ortemperature sensors are directly fed.

The, on occasion, at least two measuring device electronics, orelectronics subcomponents, 100 ₁, 100 ₂ are to be so coupled together inmanner known to those skilled in the art that, during operation of atleast one of the two measuring device electronics 100 ₁, 100 ₂,correspondingly produced measurement data can be transmitted at leastunidirectionally to the other, functioning, thus, as master electronics.This can be done, in manner known to those skilled in the art, in theform of measurement signals coded in their voltage, their current and/ortheir frequency and/or in the form of measured-values encapsulated inthe form of digitally coded telegrams, e.g. in the HART®-MULTIDROPmethod or in the burst-mode method. Of course, instead of this, however,also data connections communicating bidirectionally between the twomeasuring device electronics 100 ₁, 100 ₂ can be used for transmissionof the locally ascertained, measured variables to, in each case, theother measuring device electronics 100 ₁, 100 ₂, respectively, forexample via external fieldbus. For implementing the necessarycommunication connection between the two measuring device electronics100 ₁, 100 ₂, it is possible to apply, in advantageous manner, standardinterfaces correspondingly established in industrial measurements andautomation technology, such as e.g. line-conveyed, 4-20 mA, currentloops, on occasion also in connection with HART® or other applicablefieldbus protocols and/or suitable radio connections.

In a further advantageous embodiment of the invention, the at least onemeasuring electronics 100 ₁, 100 ₂ is additionally so designed, that itcommunicates, at least at times, as indicated schematically in FIG. 1,with a data processing system superordinated thereto, and, indeed, in amanner such that, at least in normal measuring operation,measured-values repetitively ascertained on the part of the measuringsystem are transferred, on occasion even in the form of a digitallycoded telegram, as near-time as possible and/or in real time, to thedata processing system. For registering measured-values transmitted fromthe measuring electronics, data processing system 2 is additionallyprovided with at least one evaluating circuit 80 suitably communicating,at least at times, therewith. The superordinated data processing system2 can be, for example, part of a process-near, automatic control unit oralso a long-distance process control system having a plurality ofprocess control computers and/or digital programmable logic controllers,which are arranged spatially distributed within an industrial plant andcoupled together via a corresponding data transmission network,especially also by means of digital fieldbusses. Equally, the dataprocessing system can be connected with further measuring devices and/orwith control devices, such as e.g. valves or pumps, involved in theprocess. In a further development of the invention, the data processingsystem further includes at least one fieldbus FB, especially a serialfieldbus, serving for the transmission of digital measurement- and/oroperational-data. The at least one fieldbus FB can be, for example, oneoperating according to one of the standards established in industrialprocess automation, such as e.g. FOUNDATION FIELDBUS, PROFIBUS, CANBUS,MODBUS, RACKBUS-RS 485 or the like. In an advantageous furtherdevelopment, it is, in such case, additionally provided that theaforementioned evaluation circuit 80 is coupled to the at least onefieldbus, especially for forwarding of measured-values received in theform of digital measurement data from the measuring system. Depending onhow fieldbus and measuring electronics are embodied, the latter can beconnected to the data processing system 2 either directly or by means ofan adapter, which suitably converts the signal carrying themeasured-value.

The measuring electronics and the data processing system 2 distanced, onoccasion considerably, spatially therefrom are, in a further developmentof the invention, connected electrically together by means of at leastone line-pair 2L, through which current I, especially a variable currentI, flows, at least at times, during operation. The current can be fed,for example, from an external electrical energy, or power, supply 70provided in the superordinated data processing system. During operation,supply 70 provides at least one supply voltage U_(v), especially auni-polar supply voltage, driving a current I flowing in the line-pair2L. The energy source can, in such case, be e.g. a battery and/or adirect or alternating voltage source circuit fed via a plant-internalsupply grid. For connecting, especially releasably connecting, of the atleast one line-pair 2L to the measuring electronics 100 and, thus, themeasuring system 1 itself, such further includes at least one,externally accessible, terminal pair.

For the above-described case of the measuring electronics assembledmodularly of separate subcomponents, each of the subcomponents 100 ₁,100 ₂ can, for example, be connected separately to the external energysupply, for example also by means of the aforementioned 4-20 mA currentloop. Alternatively thereto or in supplementation thereof, however, alsoone of the subcomponents 100 ₁, 100 ₂ can be so connected to the otherthat it can feed such, at least at times, with electrical energy.

The measuring electronics is, in a further embodiment, additionally soembodied that the measured-values generated internally in the measuringsystem, be it, now, measured-values of a single, registered, measuredvariable or measured-values of diverse, registered, measured variables,such as e.g. the ascertained density and an ascertained mass flow, aretransmitted at least in part, via the at least one line-pair 2L to thesuperordinated data processing system 2. The pair of electrical lines 2Lcan, in such case, be part of a so-called two-conductor current loopwell proven in industrial measurements technology. For this case, then,on the one hand, the measured-values, produced at least at times, aretransmitted via this single line-pair 2L to the superordinated dataprocessing system in the form of a load modulated (for example, by meansof conventional coupling circuits) loop current, especially a clocked orcontinuously variable, loop current, and, on the other hand, themeasuring electronics, and, thus, the measuring system, are supplied, bymeans of a corresponding, especially clocked, DC inverter, at least attimes and/or at least in part, with electrical energy, or electricalpower I_(N)·U_(N), via the line pair 2L.

The measuring electronics 100 is, in a further embodiment of theinvention, additionally designed for generating, during operation, aplurality of measured-values, especially digital measured-values,representing, at least in part, the at least one measured variable andfor transmitting such, at least partially, via terminals and the linepair 2L appropriately connected thereto, to the connected dataprocessing system 2 in a form appropriate for the data processing system2. In case required, the measuring system can, in this connection, befurther developed such that the measuring electronics 100 and dataprocessing system 2 are also connected together by means of at least oneadditional, second line pair (not shown), through which, duringoperation, at least at times, an electrical current correspondinglyflows. For this case, the measuring system can further transmit theinternally generated measured-values, at least partially also via theadditional line-pair to the data processing system. Alternativelythereto or in supplementation thereof, measuring system and dataprocessing system can also communicate with one another wirelessly, forexample by means of radio waves. Especially for this last case, it canalso be of advantage to supply the measuring system with electricalenergy, especially also exclusively, by means of an internal and/orexternal, especially replaceable and/or re-chargeable, battery and/orfuel cell. Moreover, the measuring system can additionally be fed,partially or exclusively, by means of power converters usingregenerative energy sources and placed directly on the field measuringdevice and/or placed remotely therefrom, examples of such powerconverters being e.g. thermogenerators, solar cells, wind generators,and the like.

In a further embodiment of the invention, it is provided that themeasuring system can exchange via the measuring electronics, at least attimes, with an external service- and control-unit, for example ahandheld service unit, or a programming device provided in thesuperordinated data processing system, device-specific data, such assettings-parameters, internal to the measuring device, for the measuringelectronics itself and/or diagnostic parameters internal to themeasuring system. For this purpose, provided in the measuringelectronics 100 is, additionally, at least one communication circuitCOM, which controls communications on the at least one line pair 2L.Especially, the communication circuit serves for converting themeasuring-system-specific data to be sent, into signals transmittablevia the pair 2L of electrical lines and to then couple such signals intothe lines. Alternatively thereto or in supplementation thereof, thecommunication circuit COM can, however, also be designed for receivingmeasuring system specific data, for example a set of settings-parametersto be changed for the measuring electronics, sent from the exterior viathe pertinent pair of electrical lines. The communication circuit can bee.g. an interface circuit working according to theHART®-Field-Communications-Protocol (HART Communication Foundation,Austin, Tex.), which applies high frequency, FSK-coded (frequency shiftkeying), alternating voltages as signal carrier, or, however, also oneworking according to the PROFIBUS standard. In case required, also,additionally, externally running (for example in a runtime environmentof the superordinated data processing system) processes communicatingwith the measuring electronics 100 and processing data can have directaccess to the measuring electronics.

In the case of the measuring system of the invention, it is furtherprovided that the measuring electronics produces during operation, withapplication at least of the temperature measurement signal x_(θ) as wellas the pressure measurement signal x_(p), the density measured-valueX_(ρ) in such a manner that it represents an instant, local density,which the flowing medium actually has at an imagined reference point(which can also be predeterminably spaced from the real pressuremeasuring point and/or the real temperature measuring point along theflow axis) defined locally within the process line 20. This imaginedreference point, in the absence of a corresponding density sensorthereat and for distinguishing from the actually formed and, thus, realmeasuring points provided by means of the temperature sensor andpressure sensor, respectively, is referred to as a virtual densitymeasuring point M′_(ρ). The virtual density measuring point M′_(ρ) can,in such case, both be referenced to a reference point selected duringoperation from a plurality of predetermined reference points and, thus,be locationally variable in defined manner and it can also be keptlocationally fixed. At least for the last case, a further embodiment ofthe invention provides that the electronics housing, with the measuringelectronics located therein, is placed in the immediate vicinity of thevirtual density measuring point M′_(ρ). The definition of the virtualdensity measuring point M′_(ρ) occurs, in such case, by a correspondingconfiguration of the measuring electronics, especially the calculativemethod executed therein for purposes of the density measurement, takinginto consideration position and geometric character of the realmeasuring points M_(p), M_(θ). In such case, according to a furtherembodiment of the invention, it is provided that the virtual densitymeasuring point M′_(ρ) is situated upstream of the temperature measuringpoint M_(θ) and/or upstream of the pressure measuring point M_(p).Furthermore, it can be of advantage for ascertaining the density, topermit the density measuring point to coincide either with thetemperature measuring point or with the pressure measuring point.

In the case of the measuring system being discussed, it is presumed, insuch case, that the flowing medium has at least one state variable, forexample a temperature and/or a pressure and/or a density, and/or aReynolds number Re, which, singly or together, assume(s), at the virtualdensity measurement point M′_(ρ), at least at times, especially in thetime period relevant for production of the density measured-value and/orrepetitively, an, at least in the sense of a measurement accuracydesired for the density measurement, significantly different magnitudethan at least one of the real measuring points delivering actualmeasurement signals, thus, the temperature measuring point and/or thepressure measuring point. In other words, one proceeds with theunderstanding that the medium at the virtual density measuring point is,at least at times, in a thermodynamic state and/or in a flow state,which differ(s) significantly, especially to a degree significant for adesired measuring accuracy of the measuring system, as regards at leastone, local, thermodynamic state variable (temperature, pressure,density, etc.) from a thermodynamic state of the medium at thetemperature measuring point and/or from a thermodynamic state of themedium at the pressure measuring point. This spatial variance ofthermodynamic state and/or flow state in the flowing medium can arise,as already mentioned, e.g. in the case of a compressible medium, amedium reacting in the process line, an additionally cooled medium or anadditionally heated medium. Moreover, such a variance of thermodynamicstate and/or flow state can also be brought about by allowing the mediumto flow through a process line which is sectionally narrowing and/orsectionally widening along the flow axis, such as is the case, forexample, in the application of nozzles or diffusers in the process line,so that the medium is accelerated or decelerated, on occasionaccompanied by a compression or an expansion of the same.

In an embodiment of the invention, it is, therefore, additionallyprovided that the measuring electronics, based on the pressuremeasurement signal as well as the temperature measurement signal,ascertains first a provisional density measured-value X′_(ρ), forexample according to one of the mentioned industrial standards AGA 8,AGA NX-19, SGERG-88 IAWPS-IF97, ISO 12213:2006, for representing adensity which the flowing medium solely apparently has at the virtualdensity measurement point, this because of preliminarily neglecting thespatial variances being discussed as regards the thermodynamic stateand/or the flow state.

The ascertaining of the provisional density measured-value X′_(ρ) can,in such case, be accomplished, at least at times, especially also for atleast partially gaseous media, such as natural gas, air, methane,phosgene, etc., based on the formula:

$\begin{matrix}{X_{p}^{\prime} = {\frac{n}{z \cdot R_{M}} \cdot \frac{X_{p}}{X_{\vartheta}}}} & (1)\end{matrix}$

wherein n is a molar mass, z a real gas factor of the medium ascertainedaccording to one of the industry standards AGA 8, AGA NX-19, SGERG-88IAWPS-IF97, ISO 12213:2006 and/or with application of the temperaturemeasurement signal and/or the pressure measurement signal, and R_(M) therelative gas constant of the medium, corresponding to the absolute gasconstant R normalized with the molar mass n of the medium, thus R/n,with R=8.3143 J/(K mol).

Alternatively thereto or in supplementation thereof, the measuringelectronics can ascertain the provisional density measured-value X′_(ρ),at least at times, especially in the case of media containing, at leastin part, steam, based on the formula:

$\begin{matrix}{X_{p}^{\prime} = {{\pi_{{IAWPS} - {{IF}\; 97}} \cdot \gamma_{{IAWPS} - {{IF}\; 97}}} = {\frac{X_{p}}{P_{{IAWPS} - {{IF}\; 97}}^{*}} \cdot \frac{g_{{IAWPS} - {{IF}\; 97}}}{R_{M} \cdot X_{\vartheta}}}}} & (2)\end{matrix}$

wherein π_(IAWPS-IF97)=X_(p)/P*_(IAWPS-IF97) andγ_(IAWPS-IF97)=g_(IAWPS-IF97)/(R_(M)*X_(θ)), with P* being amedium-specific, critical pressure according to the industrial standardIAWPS-IF97, especially 16.53 MPa, for the case in which the medium to bemeasured is water, above which the medium to be measured cannot beliquid, and g_(IAWPS-IF97) a medium-specific, free enthalpy (Gibbs freeenergy) according to the industrial standard IAWPS-IF97.

Selection of the currently actually suitable, calculative formula forthe provisional density measured-value X′_(ρ) and, thus, in the end,also for the actual density measured-value X_(ρ) can, in such case, beaccomplished automatically and/or in dialog with the user on-site, or,via a superordinated data processing system, semi-automatically, onoccasion also taking into consideration the currently measured pressureand the currently measured temperature and/or according to the selectionmethod proposed in the initially mentioned WO-A 2004/023081.

In a further embodiment of the invention, it is additionally providedthat the measuring electronics produces the density measured-value alsowith application of at least one numerical compensation factor K, forexample a digitally stored compensation factor, corresponding with ameasuring-system-specific and medium-specific, locational variabilityarising along the flow axis of the medium for at least one thermodynamicstate variable of the medium, especially temperature, pressure ordensity itself, and/or corresponding with a measuring-system-specificand medium-specific, locational variability arising along the flow axisof the medium for the Reynolds number of the flowing medium.

The aforementioned locational variabilities and, as a result, thecompensation factor K can, in such case, be determined in advance, atleast for measuring systems with conditions remaining constant, and/or,during operation, for example taking into consideration the mediumactually to be measured, especially its chemical composition and/or itsthermodynamic properties. The ascertaining of the compensation factor Kcan occur e.g. during a calibration of the measuring system with knownreference medium and/or during start-up of the measuring system on-site.For certain applications, especially with media of chemical compositionwhich remains constant and thermodynamic properties which remainconstant, it can be quite sufficient to ascertain the at least onecompensation factor K at least once, solely during start-up of themeasuring system. In the case of media changing significantly duringoperation of the measuring system as regards composition and/orthermodynamic properties, on occasion also as a result of replacement ofthe same, it can, however, be quite advantageous to have the measuringelectronics ascertain the compensation factor K repetitively alsofollowing the start-up, during operation of the measuring system. Theascertaining of the compensation factor K can, in such case, be carriedout on the basis of a predetermined (on occasion ascertained in dialoguewith the user, on-site or remotely, and/or externally of the measuringelectronics) specific heat capacity, c_(p), of the current medium. Forexample, the heat capacity, c_(p), or also other parameters forspecifying the medium currently to be measured, can be transmitted fromthe superordinated data processing system to the measuring electronicsand thus, as well, to the measuring system.

In another further development of the invention, the measuringelectronics includes, especially for simplifying the ascertaining of thecompensation factor K, at least one data memory 16, especially anon-volatile data memory, for storing measurement system parametersrequired for operating the measuring system, especially for defining itsmeasuring and transmitting functionalities. Especially, it is, in suchcase, further provided that the data memory, for example a data memoryin the form of a table memory and/or a non-volatile memory, stores, atleast at times, the at least one compensation factor K, if necessary,also when the measuring electronics is turned off. For example, the datamemory can store for such purpose also a plurality of compensationfactors ascertained for a different media and/or for differentcircumstances of installation, so that the measuring electronics canselect from a plurality of compensation factors stored in the datamemory the at least one currently appropriate compensation factor K,taking into consideration the current medium as well as the currentcircumstances of installation.

Especially also for ascertaining the compensation factor K, a furtherembodiment of the invention additionally provides that the data memorystores, at least at times, at least one measuring system parameterSP_(M) of a first kind solely specifying the medium currently to bemeasured and that the measuring electronics ascertains the densitymeasured-value X_(ρ) with application at least of the at least onemeasuring system parameter SP_(M) of the first kind. The measuringsystem parameter SP_(M) of the first kind can be, for example, aspecific heat capacity, c_(p), of the medium currently to be measured, amolar mass, n, of the medium and/or the number, f, of oscillatorydegrees of freedom of the atoms or molecules of the medium, asdetermined by the molecular structure of the medium, and/or parametersderived therefrom, such as e.g. the real gas or also (super-)compressibility factor, on occasion also ascertained according to one ofthe industrial standards AGA 8, AGA NX-19, SGERG-88 IAWPS-IF97, ISO12213:2006. As a result, it is clear that, accordingly, also two or moreof such measuring system parameters SP_(M) of the first kind, ofdifferent dimensions and/or units of measurement, can be stored in thedata memory for specifying the medium currently to be measured.

In a further embodiment of the invention it is additionally providedthat the data memory stores, at least at times, at least one measuringsystem parameter SP_(ME) of the second kind specifying both the mediumcurrently to be measured as well as also instantaneous circumstances ofinstallation of the measuring system, and that the measuring electronicsascertains the density measured-value X_(ρ) with application at least ofthe measuring system parameter SP_(ME) of the second kind and,especially, however, also with application of the measuring systemparameter SP_(M) of the first kind. The circumstances of installationare, in such case, determined, at least to a degree significant for theascertaining of the density measured-value, by the arrangement ofpressure-, temperature- and/or density measuring point(s) relative toone another, as well as, in each case, by the form and size of theprocess line in the region of the pressure-, density- and/or temperaturemeasuring point(s). Consequently, the measuring system parameter SP_(ME)of the second kind can be, for example, a part of a parameter setreflecting the measuring points as regards their actual positions andactual character of the process line in the region of the measuringpoints, as well as also the thermodynamic properties of the mediumcurrently to be measured, or also can be a numerical value of a complexparameter appropriately taking into consideration such influences,definitively ascertained, for example experimentally and/or empirically,first during operation of the measuring system, on occasion also withapplication of the measuring system parameter SP_(M) of the first kind.

In a further embodiment of the invention, it is additionally providedthat the measuring electronics receives, at least at times, especiallytelegraphed from the superordinated data processing system and/orascertained in near-time, numerical parameter values for at least onemedium to be measured and/or measuring system parameters SP_(M), SP_(ME)specifying instantaneous circumstances of installation of the measuringsystem, for example, thus, the heat capacity, c_(p), for medium to bemeasured currently and/or in the future. The heat capacity, c_(p), oralso an equally transmitted, other system parameter S_(M) of the firstkind can, in such case, be ascertained in advance by a correspondingmeasurement performed, for example, by the density measuring pointand/or also externally of the measuring system and/or by an input fromthe user-side, on occasion also with application of the superordinateddata processing system. Further, it is, therefore, also provided in themeasuring system of the invention that the measuring electronicscommunicating, at least at times, by line or by radio, with thesuperordinated, electronic, data processing system transmits the densitymeasured-value to the data processing system and/or that the measuringelectronics, at least at times, receives, from the data processingsystem, numerical parameter values, especially in the form of astandardized telegram, for the medium currently to be measured, forexample, thus, measuring system parameters SP_(M) of the first kindspecifying its thermodynamic properties and/or its chemical composition.If required, it is also additionally possible to ascertain, by means ofthe data processing system, measuring system parameters SP_(ME) of thesecond kind and to transmit such in the form of numerical parametervalues directly to the measuring electronics.

For the described case, in which the measuring electronics is toautomatically ascertain during operation, on the basis of systemparameters S_(M) of the first kind, at least at times, the specific heatcapacity, c_(p), of the medium currently to be measured, such can bedone, for example, based on the formula:

$\begin{matrix}{{c_{P} = {\left( {1 + \frac{f}{2}} \right) \cdot \frac{R}{n}}},} & (3)\end{matrix}$

wherein n is the measuring system parameter, molar mass, R, the absolutegas constant, with R=8.3143 J/(K·mol), and f, the measuring systemparameter, number of oscillatory degrees of freedom of the atoms ormolecules of the medium currently to be measured.

In a further embodiment of the invention, it is provided that thecompensation factor is determined solely by the medium currently to bemeasured, especially its chemical composition, as well as the physicalproperties derived directly therefrom, as well as the concreteembodiment of the measuring system as regards installation sizes andinstalled positions of the individual measuring points, as well as sizeand form of the process line in the region of the measuring points, sothat it, in the end, is largely independent of the really measured,measurement variables, pressure and temperature.

On account of, and considering, the fact that the variance of thethermodynamic state, or the flow state, of the flowing medium and, inaccompaniment therewith, the measurement accuracy of such measuringsystems can be quite co-determined also by the actual flow velocity ofthe medium, a further embodiment of the invention additionally providesthat the measuring electronics ascertains the density measured-valueX_(ρ) with application at least of a density correction value X_(K)ascertained during run-time and depending both on a flow velocity of themedium and also on the local temperature reigning at the temperaturemeasuring point. This density correction value X_(K) is, in such case,so embodied that it corresponds with an instantaneous local variabilityat least of a thermodynamic state variable of the medium, especiallysuch as depends on the medium currently to be measured as well as oninstantaneous circumstances of installation and/or which correspondswith an instantaneous local variability of the Reynolds number of theflowing medium, especially such as results from the medium and/or theconstruction of the measuring system and occurs along the flow axis ofthe measuring system.

For this, a further embodiment of the invention provides that available,at least at times in the measuring electronics, is a correspondingvelocity measured-value X_(v) representing instantaneously, as currentlyas possible, a flow velocity of the medium flowing in the measuringsystem.

With application of the velocity measured-value X_(v) and thetemperature measured-value X_(θ), as well as the already mentioned,compensation factor K, then, the density correction value X_(K) can bevery simply ascertained by means of the measuring electronics based onthe formula

$\begin{matrix}{X_{K} = {\frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}.}} & (4)\end{matrix}$

At least for the above-described case, in which the measuringelectronics 100 ascertains the provisional density measured-value X′_(ρ)by means of a calculative algorithm based on the calculative formula (1)and/or on the calculative formula 2, the density measured-value X_(ρ)for the virtual measured density can be very simply and rapidlyascertained with application both of the provisional densitymeasured-value X′_(ρ) and also the density correction value X_(K)additionally with the formula:

X _(ρ) =X′ _(ρ) ·X _(K).  (5)

Accordingly, in a further embodiment of the invention, the measuringelectronics is so configured that it ascertains the densitymeasured-value X_(ρ) with application of the above formulas (4), (5), aswell as (1) or (2), at least at times, based on the formula:

$\begin{matrix}\begin{matrix}{X_{\rho} = \frac{n \cdot X_{p}}{z \cdot R_{M} \cdot \left( {X_{\vartheta} + {K \cdot X_{v}^{2}}} \right)}} \\{= {\frac{n \cdot X_{p}}{z \cdot R_{M} \cdot X_{\vartheta}} \cdot \frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}}}\end{matrix} & (6)\end{matrix}$

and/or, at least at times, based on the formula:

$\begin{matrix}\begin{matrix}{X_{\rho} = {\pi_{{IAWPS}\text{-}{IF}\; 97} \cdot \gamma_{{IAWPS}\text{-}{IF}\; 97} \cdot \frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}}} \\{= {\frac{X_{\rho}}{P_{{IAWPS}\text{-}{IF}\; 97}^{*}} \cdot \frac{g_{{IAWPS}\text{-}{IF}\; 97}}{R_{M} \cdot X_{\vartheta}} \cdot {\frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}.}}}\end{matrix} & (7)\end{matrix}$

For testing the plausibility of the instantaneously ascertained, densitymeasured-value, for example in the course of a self-validation of themeasuring system, the measuring electronics, in a further, advantageousembodiment of the invention, compares the density correction value X_(K)during operation repetitively with at least one reference value specificto the predetermined measuring system. Developing this further, in suchcase, it is provided that the measuring electronics, based on thecomparison of density correction value X_(K) and reference value,quantitatively signals an instantaneous deviation of the densitycorrection value X_(K) from the reference value and/or, at times,generates an alarm signaling an undesired, especially unallowably high,discrepancy between density correction value X_(K) and associatedreference value. Alternatively thereto or in supplementation thereof,the measuring electronics is additionally so embodied that itascertains, repetitively during operation, a density error, whichcorresponds with a deviation, especially a relative deviation, ofprovisional density measured-value X′_(ρ) and density measured-valueX_(ρ), especially such values ascertained according to standards in theabove sense, and also issues such in the form of a numerical densityerror value. An impermissibly high discrepancy between provisionaldensity measured-value X′_(ρ) and density measured-value X_(ρ), orbetween density correlation value X_(K) and associated reference value,can, for example, be attributed to an erroneously parametered measuringelectronics, or an unexpected change of the medium to be measured and/ora disturbance of a plant containing the process line. In view of this,in an embodiment of the invention, it is provided that the measuringelectronics only applies the density correction value X_(K) in thegenerating of the density measured-value X_(ρ) when it amounts to atleast one, especially lies in a range between 1 and 1.2. In anembodiment alternative thereto, the measuring electronics is soconfigured that it applies the density correction value X_(K) in thegeneration of the density measured-value X_(ρ) only when it amounts to,at most one, especially lying in a range between 0.8 and 1.Additionally, it can be of advantage for the user, when the measuringelectronics outputs the instantaneous density error in the form of anumerical density error value and/or compares the instantaneous densityerror with at least one predetermined reference value and, based on thiscomparison, generates, at times, an alarm, which signals the undesired,especially impermissibly high, discrepancy between provisional densitymeasured-value X′_(ρ) and density measured-value X_(ρ), for example,on-site, by means of the display element HMI.

In a further development of the invention, the measuring systemadditionally delivers at least one flow measurement signal x_(v)influenced by the local flow velocity. This is done especially also forthe purpose of automatic and near-time ascertaining of the densitycorrection value X_(K). In order to accomplish the delivery of this atleast one flow measurement signal x_(v), the measuring system isequipped with at least one flow sensor placed at a velocity measuringpoint M_(v) for reacting primarily to a local flow velocity of themedium to be measured, especially to a flow velocity averaged over across section of the process line, especially also to changes of theflow velocity. During operation, measuring electronics 100 and flowsensor therefore communicate, at least at times, with one another, atleast in a manner such that the measuring electronics has available toit, at least at times, the flow measurement signal x_(v) generated bythe flow sensor. Especially, it is, in such case, additionally providedthat the measuring electronics ascertains the density measured-valueX_(ρ) also with application of the flow measurement signal. At leasttherefor, the measuring electronics communicates, at least at times,also with the flow sensor, e.g. also via external fieldbus and/orwirelessly by radio. Furthermore, it is provided that the densitymeasured-value is generated by means of the measuring device electronicsin such a manner that it represents a locational density of the mediumin the region of the flow sensor.

In the example of an embodiment shown here, at least the flow sensor,especially, however, also one of the electronics modules of themeasuring electronics, is provided by means of an industrial grade,in-line, measuring device for flowing media, for instance one embodiedas a compact device. The in-line measuring device includes at least one,essentially rigid and sufficiently pressure resistant, carrier tube,through which the medium to be measured flows during operation,especially a carrier tube inserted into the course of the process lineand, thus, forming a line-segment of the same. On and/or in the carriertube is appropriately placed the actual flow sensor. Depending onapplication, the carrier tube can be made, for example, of metal,plastic and/or ceramic.

In the case of the example of an embodiment shown here by way ofexample, the flow sensor is provided by a compact in-line measuringdevice in the form of a vortex flow meter inserted into the course ofthe process line. Such vortex flow meters serve, conventionally, forregistering, highly accurately, as primary physical, measured variable,a flow velocity and/or volume flow of flowing media, especially media ofhigh temperature and/or high pressure.

The views selected in FIGS. 3 a and 3 b show the vortex flow meterperspectively in section, in one case seen in the flow direction (FIG. 3a) and, in the other case, seen counter to the flow direction (FIG. 3b). The vortex flow meter includes a vortex sensor 30 fixed on a tubewall 21 of a carrier tube 20 serving as a line segment of the processline. Vortex sensor 30 extends through a bore 22 formed in tube wall 21and serves as flow sensor in the above sense. Vortex sensor 30 can be,for example, a dynamically compensated, vortex sensor having a paddleimmersed in the medium and a capacitive transducer element registeringits deformations, as such is also described in U.S. Pat. No. 6,003,384.

In the interior of the carrier tube 20, which itself is inserted intothe pipeline, for example, by means of appropriate flange connections,additionally arranged along one of the diameters of the carrier tube isa bluff body 40, which is securely connected with the carrier tube 20 atdiametrally oppositely lying, securement locations 41, 41*. The centerof the bore 22 and the center of the securement location 41 lie on ageneratrix of the carrier tube 20. Bluff body 40 includes an impingementsurface 42, against which medium to be measured flows during operation.Bluff body 40 has, additionally, two side surfaces, of which only afacing side surface 43 is visible in FIGS. 3 a and 3 b. Formed by theimpingement surface 42 and the side surfaces are two separation edges,of which only a facing separation edge 44 is visible completely in bothviews, while the location of the rear separation edge is evident in FIG.3 a. Bluff body 40 of FIGS. 3 a and 3 b has, here, essentially the formof a right, triangular column, thus a perpendicular column of triangularcross section. In case required, of course, also bluff bodies of othershape can be applied for implementing the measuring system of theinvention.

By the flowing of the medium against the impingement surface 42, thereforms downstream of the bluff body, in known manner, a Karman vortexstreet, in that vortices separate alternately at each separation edgeand then proceed downstream in the flowing medium. These vorticesentrained by the flow produce, in turn, local pressure fluctuations inthe flowing medium and their time-referenced separation frequency, thustheir so-called vortex frequency, is a measure for the flow velocityand/or the volume flow of the medium. The pressure fluctuations releasedfrom the entrained vortices are then converted by means of the vortexsensor 30, formed, here, by means of paddle and placed downstream of thebluff body, into a vortex signal corresponding to the local flowvelocity and serving as electrical, flow measurement signal x_(v).

The transducer element 36 produces the above-mentioned measurementsignal, whose frequency is proportional to the volume flow of theflowing medium.

The vortex sensor 30 is inserted downstream of the bluff body 40 intothe bore 22 in the tube wall 21 of the carrier tube 20 and seals thebore 22 against escape of medium from the interior of the carrier tube20 to the outer surface of the carrier tube 20, this being accomplishedby a screwed engagement of the vortex sensor 30 with the wall 21.Serving for this are e.g. four screws, of which the screws 5, 6, 7 arevisible in FIGS. 3 a and 3 b. Parts of the vortex sensor visible inFIGS. 3 a and 3 b are the wedge-shaped sensor vane 31 extending into theinterior of the carrier tube 20 through the bore 22 of the tube wall 21and a housing cap 32. Housing cap 32 runs out to an extension 322, withinterposition of a thin-walled intermediate piece 323; compare, in thisconnection, also the already mentioned U.S. Pat. No. 6,003,384. Sensorvane 31 has principal surfaces, of which only the principal surface 311is visible in FIGS. 3 a and 3 b. The principal surfaces are aligned withthe mentioned generatrix of the carrier 20 and form a front edge 313.Sensor vane 31 can also have other spatial forms; thus, e.g., it canhave two parallel principal surfaces, which form two parallel frontedges. Sensor vane 31 is shorter than the diameter of the carrier tube20; it is, furthermore, flexurally stiff and can include, for example, ablind hole, in which a transducer element can be inserted, in the formof a thermocouple or resistance thermometer serving to detect thetemperature of the medium, on occasion for generating the temperaturemeasurement signal and, thus, also for implementing the temperaturemeasuring point itself; compare, in this connection, also the alreadymentioned U.S. Pat. No. 6,988,418 or U.S. Pat. No. 6,910,387. In orderthat the blind hole 314 has a sufficient diameter, wall portionsprotrude out of the principal surfaces, such a wall portion 315 beingindicated in FIG. 3 a. The blind hole 314 extends into the vicinity ofthe front edge 313 and has there a floor.

To the vortex sensor 30 belongs, additionally, a diaphragm 33 coveringover the bore 22 and having a first surface 331 facing the medium and asecond surface 332 facing away from the medium; see FIGS. 3 and 4.Sensor vane 31 is affixed to the surface 331, while aphysical-to-electrical transducer element 36 reacting to bending, ormovements, of vane 31 is affixed to the surface 332. Sensor vane 31,diaphragm 33, as well as its annular edge 333, can be manufactured of asingle piece of material, e.g. metal, especially stainless steel.

It is to be noted here that, instead of the vortex flow meter shown hereby way of example, having at least one bluff body protruding into alumen of the process line and immersed in the medium, and at least oneflow sensor arranged downstream of the at least one bluff body,especially a flow sensor protruding at least partially into a lumen ofthe process line, of course, also other in-line measuring devicesequally established in process automation technology can be used forproviding the at least one flow sensor delivering said flow measurementsignal and, thus, for forming the flow measuring point as such, examplesbeing e.g. magneto-inductive flow meters, thermal flow meters,pressure-difference flow meters, ultrasonic flow measuring devices, orthe like. The flow sensor itself can, in such case, as also usual in thecase of such measuring devices, and depending on the implementedprinciple of measurement, be formed by means of at least one electricalresistance element, especially one through which flows, at least attimes, a heating current, by means of at least one measuring electrodetapping electrical potentials, especially a measuring electrodecontacting flowing medium, by means of at least one measuring capacitorreacting to changes of the flow parameter, and/or by means of at leastone piezoelectric and/or piezoresistive element. The flow sensor can be,especially in the case of application of a measuring capacitor and/or apiezoelectric or piezoresistive element for forming the flow sensor, onewhich is subjected during operation repeatedly to mechanicaldeformations under action of the medium flowing in the measuring systemfor generating the measurement signal and/or which is moved duringoperation repeatedly relative to a static, rest position under action ofthe medium flowing in the measuring tube, such as is usually the case,besides the aforementioned in-line measuring devices measuring the flowparameter on the basis of vortices entrained in the flow with formationof a Karman vortex street, e.g. also for such in-line measuring deviceswhich measure flow parameters of the kind being discussed on the basisof pressure differences. For the latter case, the at least one flowsensor can be formed, for example, by means of at least one flowobstacle narrowing a cross section of the process line, especially anorifice plate or a nozzle, as well as by means of at least one pressuredifference sensor, which registers a pressure difference arising acrossthe flow obstacle and delivers a representative pressure differencemeasurement signal. The at least one pressure difference sensor can, insuch case, be formed e.g. partly by means of a pressure sensor placed atthe pressure measuring point. Alternatively to the aforementionedsensor- or measuring-device-types, the at least one flow sensor can,moreover, also be formed in conjunction with a line segment of theprocess line, wherein vibrations of such line segment, excited activelyfrom the outside by means of an oscillation exciter and/or passively bythe medium itself, are detected by means of at least one transducerelement registering, for example electrodynamically oropto-electronically, mechanical oscillations and delivering acorresponding oscillation signal, such as is known to be the case, forexample, also with Coriolis mass flow meters. Commercial Coriolis massflow meters are usually in-line measuring devices, offered as compactmeasuring devices, in which at least one measuring tube equippedexternally with oscillation exciters and sensors are inserted by meansof flanges into the course of the process line to form the line segmentvibrating, at least at times, during operation.

The application of measuring systems with an in-line measuring device ofthe aforementioned kind enables, thus, in addition to the virtuallymeasured density, other measured variables, especially a mass flow, avolume flow, a flow velocity, a viscosity, a pressure, a temperatureand/or the like, of the medium flowing in the process line equally to beascertained highly accurately, occasionally also in real time.

At least in the case of application also of a flow sensor internal tothe measuring system, it is possible, moreover, also to ascertain theabove-mentioned compensation factor K directly, in advance, especiallyalso in the course of a wet calibration. For example, compensationfactor K can be very simply so selected, that the formula

$\begin{matrix}{K = {\Delta \; X\; {\rho \cdot \frac{X_{\vartheta}}{X_{v}^{2}}}}} & (8)\end{matrix}$

is fulfilled, wherein ΔX_(ρ) corresponds to a deviation ascertained inadvance, especially in the course of a calibration of the same and/or inan essentially equal measuring system with known reference medium and/orin the course of start-up of the measuring system on-site, e.g. acalculated and/or measured, measuring-system-specific deviation, whichthe provisional density measured-value X′_(ρ), ascertained for areference medium defined at least with respect to its actual density,ρ_(Ref), has from such density ρ_(Ref) of the reference medium. As aresult, ΔX_(ρ) can be viewed practically also as the measurement errorinherent to the measuring system, i.e. the measurement error with whichthe provisional density measured-value X′_(ρ) ascertained by means ofthe measuring system itself is burdened at the virtual measuring pointin comparison with the actual density. With knowledge of the provisionaldensity measured-value X′_(ρ), as well as also the actual density,ρ_(Ref), of the reference medium, this measurement error can bequantified as follows:

$\begin{matrix}{{{\Delta \; X\; \rho} = \left( {\frac{X_{\rho}^{\prime}}{\rho_{Ref}} - 1} \right)},} & (9)\end{matrix}$

so that the compensation factor K, as a result, is to be so selectedthat it obeys, as exactly as possible, the following formula:

$\begin{matrix}{K = {{\Delta \; X\; {\rho \cdot \frac{X_{\vartheta}}{X_{v}^{2}}}} = {\left( {\frac{X_{\rho}^{\prime}}{\rho_{Ref}} - 1} \right) \cdot \frac{X_{\vartheta}}{X_{v}^{2}}}}} & (10)\end{matrix}$

Alternatively thereto or in supplementation thereof, at least in thecase of application of a flow sensor internal to the measuring system,it is, however, also quite possible to ascertain the compensation factorK experimentally by means of a reference measuring system andcorresponding reference media and/or by computer simulation and, basedthereon, to extrapolate further numerical values for the compensationfactors K for other measuring systems similar to the reference measuringsystem and/or to other media.

In a further embodiment of the invention, it is additionally providedthat the measuring electronics, with application at least of the flowmeasurement signal, also ascertains a velocity measured-value X_(v),especially a digital, velocity measured-value X_(v), whichinstantaneously represents the flow velocity of the flowing medium,and/or that the measuring electronics, with application at least of theflow measurement signal, also ascertains a volume flow measured-valueX_(v), for example a digital, volume flow measured-value, whichinstantaneously represents a volume flow rate of the flowing medium.Alternatively thereto or in supplementation thereof, the measuringelectronics, with application at least of the temperature measurementsignal and the pressure measurement signal, or the densitymeasured-value, as well as the flow measurement signal, or the volumeflow measured-value derived therefrom, can, during operation, ascertain,further, a mass flow measured-value X_(m), for example a digital, massflow measured-value, which represents, instantaneously, a mass flowrate, or an integrated, i.e. totalized, mass flow.

For simplifying construction of the measuring system and, alongtherewith, for further improving accuracy of the density measured-value,the flow sensor can, in advantageous manner, be so placed that, asproposed, for example, also in U.S. Pat. No. 6,988,418 or U.S. Pat. No.6,910,387, at least the flow measuring point and the temperaturemeasuring point, or, as proposed, for example, also in U.S. Pat. No.7,007,556, at least the flow measuring point and the pressure measuringpoint, at least partially overlap one another, especially arecoincident. Alternatively thereto or in supplementation thereof, theflow measuring point can, however, also, as shown schematically in FIGS.1 and 2, be arranged remotely from the temperature measuring pointand/or the pressure measuring point, for example upstream of thetemperature measuring point and/or upstream of the pressure measuringpoint.

In a further embodiment of the invention, it is additionally providedthat the temperature sensor of the measuring system and/or the pressuresensor are, as proposed, for example, also in U.S. Pat. No. 6,988,418,U.S. Pat. No. 6,910,387 or U.S. Pat. No. 6,651,512, likewise provided bymeans of the in-line measuring device containing the flow sensor, forexample an in-line measuring device in the form of a compact measuringdevice.

In a further embodiment of the invention, the virtual density measuringpoint and the flow measuring point are so selected that the medium hasat the virtual density measuring point a thermodynamic statecorresponding to a thermodynamic state of the medium at the velocitymeasuring point and/or that the medium has at the virtual densitymeasuring point and velocity measuring point essentially equal Reynoldsnumbers. This can, for example, be achieved by so defining the virtualdensity measuring point that it and the flow measuring point at leastpartially overlap one another, especially are coincident. In otherwords, thus the density measured-value should be ascertained in such amanner that it exactly represents a local density of the medium in theregion of the flow sensor and consequently also exactly represents thelocal density of the medium at the velocity measuring point.

For further simplifying the measuring, another embodiment of themeasuring system provides that the process line is an essentiallystraight pipeline, thus no elbows or bends, at least sectionally,especially in the region between density measuring point and pressuremeasuring point and/or between density measuring point and temperaturemeasuring point. Moreover, the process line should be embodied, at leastsectionally, especially in the region of the temperature measuring pointand/or in the region of the pressure measuring point, as an essentiallyform-stable pipeline, at least under operating pressure, especially arigid pipeline and/or a pipeline circular in cross section.

In a further embodiment of the invention, the aforementioned variance isproduced during operation in largely defined manner by providing theprocess line, at least at the virtual density measuring point,additionally with a caliber D1 differing from a caliber D2 of theprocess line at the pressure measuring point. Alternatively thereto orin supplementation thereof, another embodiment of the inventionadditionally provides that the process line has at the virtual densitymeasuring location a caliber D1 differing from caliber D3 of the processline at the temperature measuring point, and/or that the caliber D2 ofthe process line at the pressure measuring point is different from thecaliber D3 of the process line at the temperature measuring point. Indetail, thus, a large number of possibilities of combination results asregards the arrangement of the individual measuring points relative toone another, as well as also the choice of caliber of the process lineat the particular measuring points. A selection of especially suitedvariants of embodiment herefor is, moreover, also shown schematically inFIGS. 4 a, 4 b, 4 c, 4 d, 4 e, 4 f and 4 h.

As shown therein, it can be of advantage to embody the measuring systemsuch that the caliber D2 of the process line is greater at the pressuremeasuring point than the caliber D3 of the process line at thetemperature measuring point, or, however, also such that the caliber D3of the process line at the temperature measuring point is greater thanthe caliber D2 of the process line at the pressure measuring point.Alternatively thereto or in supplementation thereof, the caliber D2 ofthe process line at the pressure measuring point can also be so selectedthat it is greater than the caliber D1 of the process line at thevirtual density measuring point and/or the caliber D3 of the processline at the temperature measuring point can be so selected that it isgreater than the caliber D1 at the virtual density measuring point.Especially, it is further provided that a caliber ratio D3/D1 of thecaliber D3 of the process line at the temperature measuring point to thecaliber D1 of the process line at the virtual density measuring point isgreater than 1.1 and/or smaller than 5, for example thus lying in arange between 1.2 and 3.1. Further, it is at least for this case, ofadvantage when the process line at the virtual density measuring pointhas a caliber D1, which is essentially equal to a caliber D2 of theprocess line at the temperature measuring point. In another embodimentof the invention, it is provided that a caliber ratio D2/D1 of thecaliber D2 of the process line at the pressure measuring point to thecaliber D1 of the process line at the virtual density measuring point iskept greater than 1.1 and/or smaller than 5, for example thus lying in arange between 1.2 and 3.1. For this case it is, in turn, of advantagewhen the process line at the virtual density measuring point has acaliber D1, which is essentially equal to a caliber D3 of the processline at the temperature measuring point.

The differences between the calibers D1, D2, D3, respectively, can,depending on desired configuration, be implemented by providing theprocess line between at least two of the aforementioned measuringpoints, for example thus between the virtual density measuring point andthe temperature measuring point and/or the pressure measuring point, oralso between the temperature measuring point and the pressure measuringpoint, with a line segment embodied as a diffuser, especially afunnel-shaped diffuser, having a lumen widening in the flow direction,especially continuously widening in the flow direction, or a linesegment which is formed as a nozzle, especially a funnel-shaped nozzlehaving a lumen narrowing in the flow direction, especially continuouslynarrowing in the flow direction.

Experimental investigations have shown further that the measuring pointsshould, in advantageous manner, be so placed, or defined, that adistance L21 of the pressure measuring point from the virtual densitymeasuring point differs from a distance L31 of the temperature measuringpoint from the virtual density measuring point. For example, it can bequite advantageous for the measurement, when the distance L21 of thepressure measuring point from the virtual density measuring point isgreater than the distance L31 of the temperature measuring point fromthe virtual density measuring point and/or when the distance L21 of thepressure measuring point from the virtual density measuring point and/ora distance L23 of the pressure measuring point from the temperaturemeasuring point are/is greater than the caliber D2 of the process lineat the pressure measuring point. Found to be quite suitable are, in suchcase, a distance L21 and/or a distance L23 of at least three times,especially more than five times, the caliber D2.

Further information for layout and dimensioning of the process line ofthe measuring system as regards aforementioned installed lengths and/orcaliber ratios in the case of application of a reducer are and/or adiffuser, as well as also other embodiments of the process line upstreamof the flow sensor and or downstream of the flow of sensor are herebyexplicitly referenced in the assignee's not-prepublished applications DE102006034296.8 and 102006047815.0, or in subsequent applicationscorresponding therewith, whose respective disclosures are thus to beconsidered as belonging to the present application.

Further investigations with measuring systems of the invention haveshown additionally for the arrangements of temperature, pressure anddensity measuring points shown in the FIGS. 4 a, 4 b, 4 c, 4 d relativeto one another as well as with reference to the aforementioned caliberratios, that that the density correction value ascertained therefor atleast according to formula (4) and used for the ascertaining of thedensity measured-value according to the formula (1), or (2), shouldalways be greater than one; otherwise, as already mentioned, amalfunctioning measuring system or a disturbance of the plant would beassumed. Equally, for the constellations shown in FIGS. 4 e, 4 f, 4 g,and 4 h, the density correction value, assuming application of the samecalculative formulas, should always be smaller than one.

Beyond this, the following Table 1 provides constellations as regardscalibers D1, D2, D3, in each case in the units mm, and selected gases asmedium, as well as in each case a correspondingly suitable compensationfactor K in the units K·s² m⁻², especially suitable for a measuringsystem with a flow sensor according to the example of an embodimentshown in FIGS. 2 and 3.

TABLE 1 GAS D1, D3 D2 K CH₄ 13.9 24.3 27851.08558 (n = 16 g · mol⁻¹,13.9 26.7 26084.12357 f = 6) 13.9 27.2 25671.22129 13.9 28.5 24567.6518613.9 38.1 17069.51792 13.9 40.9 15350.28348 13.9 41.2 15178.90947 13.943.1 14147.85441 24.3 38.1 3086.763684 24.3 40.9 3035.482335 24.3 41.23026.384008 24.3 43.1 2957.410639 24.3 49.2 2662.97974 24.3 52.62484.170531 24.3 52.7 2478.934254 24.3 54.5 2385.462689 38.1 49.2448.2000215 38.1 52.6 487.9209744 38.1 54.5 500.3838513 38.1 73.7459.369374 38.1 78 435.8925863 38.1 78.1 435.337907 38.1 82.5410.9043438 49.2 73.7 183.0929623 49.2 78 183.4977725 49.2 78.1183.4687956 49.2 82.5 180.8940523 49.2 97 162.4571647 49.2 102.3154.3167919 49.2 102.4 154.1619225 49.2 107.1 146.8997624 73.7 9732.98911974 73.7 102.4 35.0370316 73.7 107.1 36.01526944 73.7 14632.12475476 73.7 151 31.10798557 73.7 154.2 30.45138942 73.7 159.329.40598339 97 146 12.12975471 97 151 12.16106709 97 154.2 12.1409884697 159.3 12.05687371 97 199.9 10.30674712 97 202.7 10.16121596 97 206.59.963705636 97 207.3 9.922187549 146 199.9 2.245529752 146 202.72.273600656 146 206.5 2.304852917 146 207.3 2.310502276 146 248.82.317268815 146 254.5 2.291734778 146 258.8 2.2702775 146 260.42.261877863 Natural gas 13.9 24.3 31170.01324 (n = 16 . . . 40 g ·mol⁻¹, 13.9 26.7 29190.34938 depending on composition, 13.9 27.228727.93943 f = 6) 13.9 28.5 27492.24479 13.9 38.1 19099.80535 13.9 40.917175.91318 13.9 41.2 16984.14311 13.9 43.1 15830.39114 24.3 38.13455.020015 24.3 40.9 3397.337203 24.3 41.2 3387.128821 24.3 43.13309.793458 24.3 49.2 2980.007098 24.3 52.6 2779.822049 24.3 52.72773.96038 24.3 54.5 2669.329455 38.1 49.2 501.8495813 38.1 52.6546.2444885 38.1 54.5 560.159696 38.1 73.7 514.0710105 38.1 78487.7826811 38.1 78.1 487.1616486 38.1 82.5 459.8077209 49.2 73.7204.9496071 49.2 78 205.3864268 49.2 78.1 205.3536589 49.2 82.5202.458931 49.2 97 181.8004079 49.2 102.3 172.6858252 49.2 102.4172.5124389 49.2 107.1 164.3825333 73.7 97 36.93625048 73.7 102.439.22468158 73.7 107.1 40.31654938 73.7 146 35.94964274 73.7 15134.81116896 73.7 154.2 34.07605503 73.7 159.3 32.90573249 97 14613.57764009 97 151 13.61203427 97 154.2 13.58918743 97 159.3 13.4945140597 199.9 11.53365739 97 202.7 11.37072445 97 206.5 11.14960825 97 207.311.10312955 146 199.9 2.5139906 146 202.7 2.545346756 146 206.52.580243371 146 207.3 2.586549405 146 248.8 2.593473866 146 254.52.564840534 146 258.8 2.540788021 146 260.4 2.531374101 H₂O 13.9 24.331256.24144 (n = 18 g · mol⁻¹, 13.9 26.7 29271.0454 f = 6) 13.9 27.228807.34836 13.9 28.5 27568.21927 13.9 38.1 19152.54293 13.9 40.917223.33422 13.9 41.2 17031.03432 13.9 43.1 15874.09507 24.3 38.13464.588763 24.3 40.9 3406.738816 24.3 41.2 3396.501521 24.3 43.13318.948505 24.3 49.2 2988.242826 24.3 52.6 2787.502227 24.3 52.72781.624305 24.3 54.5 2676.703394 38.1 49.2 503.2441144 38.1 52.6547.7602846 38.1 54.5 561.7131315 38.1 73.7 515.492087 38.1 78489.1306726 38.1 78.1 488.5079154 38.1 82.5 461.07809 49.2 73.7205.5175663 49.2 78 205.9551717 49.2 78.1 205.9223044 49.2 82.5203.0192259 49.2 97 182.3029139 49.2 102.3 173.1630088 49.2 102.4172.9891412 49.2 107.1 164.8366844 73.7 97 37.03884498 73.7 102.439.33351491 73.7 107.1 40.42832654 73.7 146 36.04900682 73.7 15134.90736955 73.7 154.2 34.1702149 73.7 159.3 32.99664598 97 14613.61526406 97 151 13.64973647 97 154.2 13.62681665 97 159.3 13.5318674497 199.9 11.56552973 97 202.7 11.40214452 97 206.5 11.18041482 97 207.311.1338072 146 199.9 2.52096787 146 202.7 2.552409208 146 206.52.587400279 146 207.3 2.593723327 146 248.8 2.600650057 146 254.52.571936044 146 258.8 2.547815996 146 260.4 2.538375687 Air 13.9 24.350338.90921 (n = 29 g · mol⁻¹, 13.9 26.7 47124.38089 f = 5) 13.9 27.246375.14885 13.9 28.5 44374.58191 13.9 38.1 30815.23069 13.9 40.927710.05332 13.9 41.2 27400.56851 13.9 43.1 25538.71377 24.3 38.15583.208016 24.3 41.2 5470.96068 24.3 43.1 5344.897321 24.3 49.24810.117614 24.3 52.6 4486.285526 24.3 52.7 4476.808075 24.3 54.54307.671069 38.1 49.2 812.4565419 38.1 52.6 883.65719 38.1 54.5905.8569033 38.1 73.7 829.8882553 38.1 78 787.3215533 38.1 78.1786.316573 38.1 82.5 742.0716954 49.2 73.7 331.3026455 49.2 78331.8738927 49.2 78.1 331.8181848 49.2 82.5 327.0348906 49.2 97293.4714706 49.2 102.3 278.7184046 49.2 102.4 278.437899 49.2 107.1265.289832 73.7 97 59.78309893 73.7 102.4 63.449488 73.7 107.165.18836646 73.7 146 58.03092489 73.7 151 56.18799037 73.7 154.254.9986214 73.7 159.3 53.10590103 97 146 21.94754221 97 151 21.9977143597 154.2 21.95771667 97 159.3 21.80041304 97 199.9 18.61596382 97 202.718.35235887 97 206.5 17.99471318 97 207.3 17.91954828 146 199.94.067220274 146 202.7 4.117361285 146 206.5 4.173054129 146 207.34.183100739 146 248.8 4.188923875 146 254.5 4.142218763 146 258.84.103061713 146 260.4 4.087749585

1. A measuring system for measuring a density of a medium, which isvariable as regards a thermodynamic state, especially at least partiallycompressible, flowing in a process line along a flow axis of themeasuring system, comprising: at least one temperature sensor placed ata temperature measuring point (M_(θ)), reacting primarily to a localtemperature, θ, of medium flowing past, and delivering at least onetemperature measurement signal (x_(θ)) influenced by the localtemperature of the medium to be measured; at least one pressure sensorplaced at a pressure measuring point (M_(p)), reacting primarily to alocal pressure, p, especially a static pressure, of medium flowing past,and delivering at least one pressure measurement signal (x_(p))influenced by the local pressure, p, in the medium to be measured; and ameasuring electronics communicating, in each case, at least at times,with at least the temperature sensor and the pressure sensor, andproducing, at least at times, with application both of the temperaturemeasurement signal and also at least the pressure measurement signal, aswell as with application of at least one numerical compensation factor(K), especially a digitally stored, numerical compensation factor (K),at least one density measured-value (X_(ρ)), especially a digitaldensity measured-value, representing, instantaneously, a local density,ρ, of the flowing medium at a virtual density measuring point (M′_(ρ)),especially a virtual density measuring point predeterminably spaced fromthe pressure measuring point (M_(p)) and/or the temperature measuringpoint (M_(θ)) along the flow axis; wherein: the compensation factor (K)corresponds with a locational variability of at least one thermodynamicvariable of the medium, especially a temperature, a pressure or adensity, occurring along the flow axis of the measuring system,especially as ascertained in advance and/or during operation, and/orcorresponds with a locational variability of the Reynolds number of theflowing medium along the flow axis of the measuring system, especiallyas ascertained in advance and/or during operation.
 2. The measuringsystem as claimed in claim 1, wherein: the at least one compensationfactor (K) is ascertained taking into consideration the medium actuallyto be measured, especially its composition and/or its thermodynamicproperties, especially during a calibration of the measuring system withknown reference medium and/or during start-up of the measuring systemon-site.
 3. The measuring system as claimed in claim 2, wherein: saidmeasuring electronics ascertains the at least one compensation factor(K) at least once during start-up of the measuring system, and/or saidmeasuring electronics ascertains the compensation factor (K)repetitively during operation of the measuring system, especially inconjunction with a change of at least one chemical property of themedium to be measured or with a replacement of the medium by another. 4.The measuring system as claimed in claim 3, wherein: said measuringelectronics ascertains the at least one compensation factor (K) on thebasis of a predetermined, specific heat capacity, c_(p), of the currentmedium, especially a specific heat capacity ascertained in dialog withthe user and/or externally of the measuring electronics.
 5. Themeasuring system as claimed in claim 1, wherein: said measuringelectronics includes a data memory, especially embodied as a tablememory and/or a non-volatile memory, storing the at least onecompensation factor (K).
 6. The measuring system as claimed in claim 5,wherein: the data memory stores a plurality of compensation factorsascertained in advance for different media and/or for differentcircumstances of installation.
 7. The measuring system as claimed inclaim 6, wherein: said measuring electronics selects the at least onecompensation factor (K) from a plurality of compensation factors storedin the data memory, taking into consideration the current medium, aswell as the current circumstances of installation.
 8. The measuringsystem as claimed in claim 1, wherein: said measuring electronicsincludes a data memory, especially a non-volatile data memory, whichstores, at least at times, at least one measuring system parameter(SP_(M)) specifying solely the medium currently to be measured,especially a specific heat capacity, c_(p), of the medium currently tobe measured, a molar mass, n, of the medium and/or the number, f, ofoscillatory degrees of freedom of the atoms or molecules of the medium,as determined by the molecular composition of the medium.
 9. Themeasuring system as claimed in claim 8, wherein: said measuringelectronics ascertains, with application of the at least one measuringsystem parameter (SP_(M)) specifying solely the medium currently to bemeasured, the density measured-value (X_(ρ)).
 10. The measuring systemas claimed in claim 1, wherein: said measuring electronics includes adata memory, especially a non-volatile data memory, which stores, atleast at times, a measuring system parameter (SP_(ME)) specifying boththe medium currently to be measured by means of the measuring system aswell as also instantaneous circumstances of installation of themeasuring system, wherein: the circumstances of installation aredetermined by the arrangement of pressure-, temperature- anddensity-measuring points relative to one another, as well as, in eachcase, by form and size of the process line in the region of thepressure-, density- and/or temperature-measuring points.
 11. Themeasuring system as claimed in claim 10, wherein: said measuringelectronics ascertains the density measured-value (X_(ρ)) withapplication of the at least one measuring system parameter (SP_(ME))specifying both the medium currently to be measured by means of themeasuring system as well as also instantaneous circumstances ofinstallation of the measuring system.
 12. The measuring system asclaimed in claim 1, wherein: said measuring electronics includes a datamemory, especially a non-volatile data memory, which stores, at least ittimes, at least one measuring system parameter (SP_(M)) of a first kindcurrently specifying the medium to be measured, especially a specificheat capacity of the medium currently to be measured, a molar mass ofthe system and/or the number of degrees of freedom of the medium, andwhich stores, at least a times, at least one measuring system parameter(SP_(ME)) of a second kind specifying both the medium currently to bemeasured as well as also instantaneous circumstances of installation ofthe measuring system; the circumstances of installation are determinedby the arrangement of pressure-, temperature- and pressure-measuringpoints relative to one another, as well as, in each case, form and sizeof the process line in the region of the pressure-, density-, and/ortemperature-measuring points; and the measuring electronics ascertainsthe density measured-value (X_(ρ)) with application at least of themeasuring system parameter (SP_(M)) of the first kind and the measuringsystem parameter (SP_(ME)) of the second kind.
 13. The measuring systemas claimed in claim 1, wherein: said measuring electronics receives, atleast at times, numerical parameter values, especially numericalparameter values ascertained externally at the measuring system and/orin near-time, for at least one measuring system parameter (SP_(M),SP_(ME)) specifying a medium to be measured and/or instantaneouscircumstances of installation of the measuring system, especially a heatcapacity, c_(p), for the medium to be measured, representing a specificheat capacity, c_(p), of the medium to be measured ascertained inadvance and/or measured remotely from the density measuring point. 14.The measuring system as claimed in claim 1, wherein: said measuringelectronics communicates, especially via fieldbus, at least at times,especially by wire and/or radio, with a superordinated, electronic, dataprocessing system.
 15. The measuring system as claimed in claim 14,wherein: said measuring electronics transmits the density measured-valueto the data processing system; and/or said measuring electronicsreceives from the data processing system, at least at times, numericalparameter values for the measuring system parameter (SP_(M)) specifyingmedium currently to be measured, especially its thermodynamic propertiesand/or its chemical composition, especially a measuring system parametersuch as a specific heat capacity, c_(p), of the medium currently to bemeasured, a molar mass, n, of the medium currently to be measured and/orthe number, f, of oscillatory degrees of freedom of the atoms ormolecules of the medium currently to be measured.
 16. The measuringsystem as claimed in claim 14, wherein: said measuring electronics isconnected with the superordinated electronic data processing system bymeans of a fieldbus, especially a serial fieldbus.
 17. The measuringsystem as claimed in claim 1, wherein: said measuring electronicsascertains during operation, at least it times, a specific heatcapacity, c_(p), of the medium currently to be measured, especiallybased on the formula:${c_{p} = {\left( {1 + \frac{f}{2}} \right) \cdot \frac{R}{n}}},$wherein n is a molar mass, R the absolute gas constant, with R=8.3143J/(K mol), and f a number of degrees of oscillatory freedom of atoms ormolecules of the medium, as determined by its molecular composition. 18.The measuring system as claimed in claim 1, wherein: said measuringelectronics repetitively generates, based on the temperature measurementsignal, a temperature measured-value (X_(θ)), especially a digital,temperature measured-value, representing, instantaneously, a localtemperature of the medium, especially the temperature of the medium atthe temperature measuring point.
 19. The measuring system as claimed inclaim 1, wherein: said measuring electronics generates repetitively,based on the pressure measurement signal, a pressure measurement signal(x_(p)), especially a digital pressure measurement signal, representing,instantaneously, a pressure reigning in the medium, especially apressure reigning in the medium at the pressure measuring point.
 20. Themeasuring system as claimed in claim 1, further comprising: at least oneflow sensor placed at a flow measuring point, reacting primarily to alocal flow parameter, especially a flow parameter averaged over a crosssection of the process line, especially a flow velocity, a volume flowor a mass flow of the medium to be measured, especially also to changesof the same, and delivering at least one flow measurement signalinfluenced by the local flow parameter.
 21. The measuring system asclaimed in claim 1, wherein: said measuring electronics communicates, atleast at times, also with the flow sensor; and said measuringelectronics ascertains, with application also of the flow measurementsignal, the density measured-value (X_(ρ)).
 22. The measuring system asclaimed in claim 20, wherein: the medium has at the virtual densitymeasuring point a thermodynamic state corresponding to a thermodynamicstate of the medium at the velocity measuring point.
 23. The measuringsystem as claimed in claim 20, wherein: the virtual density measuringpoint and the flow measuring point at least partially overlap oneanother, especially are coincident.
 24. The measuring system as claimedin claim 20, wherein: the temperature measuring point and the flowmeasuring point overlap one another at least partially, especially, theyare coincident.
 25. The measuring system as claimed in claim 20,wherein: the pressure measuring point and the flow measuring point atleast partially overlap.
 26. The measuring system as claimed in claim20, wherein: the density measured-value represents a local density ofthe medium in the region of the flow sensor.
 27. The measuring system asclaimed in claim 20, wherein: said measuring electronics communicates bymeans of a fieldbus, especially a serial fieldbus, and/or wirelessly byradio, with the flow sensor.
 28. The measuring system as claimed inclaim 20, wherein: said measuring electronics communicates, at least atimes, with the flow sensor; and said measuring electronics, withapplication at least of the flow measurement signal, ascertains avelocity measured-value (X_(v)), especially a digital, velocitymeasured-value, representing, instantaneously, the flow velocity of theflowing medium.
 29. The measuring system as claimed in claim 1, wherein:said measuring electronics produces the density measured-value (X_(ρ))with application of at least one density correction value (X_(K))ascertained at run time and depending on both a flow velocity of themedium as well as also on a local temperature reigning at thetemperature measuring point and corresponding with an instantaneouslocal variability of at least one thermodynamic state variable of themedium, especially such a variability as determined by instantaneouscircumstances of installation and/or occurring along the flow axis ofthe measuring system, and/or corresponding with an instantaneous localvariability of the Reynolds number of the flowing medium, especially avariability of the Reynolds number as determined by the medium and/orthe structure of the measuring system and/or occurring along the flowaxis of the measuring system.
 30. The measuring system as claimed inclaim 29 wherein: said measuring electronics ascertains the densitycorrection value (X_(K)) with application of the velocity measured-value(X_(v)) as well as the temperature measured-value (X_(θ)).
 31. Themeasuring system as claimed in claim 29, wherein: said measuringelectronics ascertains the density correction value (X_(K)) also withapplication of the at least one compensation factor (K) ascertained inadvance, especially a compensation factor stored digitally, especiallyone based on the formula$X_{K} = {\frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}.}$32. The measuring system as claimed in claim 29, wherein: said measuringelectronics compares the density correction value (X_(K)) repetitivelyduring operation with at least one predetermined, reference value. 33.The measuring system as claimed in claim 32, wherein: said measuringelectronics, based on the comparison of the density correction value(X_(K)) and reference value, quantitatively signals an instantaneousdeviation of the density correction value (X_(K)) from the referencevalue and/or generates, at times, an alarm signaling an undesireddiscrepancy, especially an impermissibly high discrepancy, betweendensity correction value (X_(K)) and associated reference value.
 34. Themeasuring system as claimed in claim 1, wherein: said measuringelectronics, based on the pressure measurement signal, as well as thetemperature measurement signal, ascertains a provisional densitymeasured-value (X′_(ρ)), especially according to one of industrialstandards AGA 8, AGA NX-19, SGERG-88 IAWPS-IF97, ISO 12213:2006, whereinthe provisional density represents a density which the flowing mediumonly apparently has at the virtual density measuring point.
 35. Themeasuring system as claimed in claim 34, wherein: said measuringelectronics ascertains the provisional density measured value (X′_(ρ)),at least at times, based on the formula:${X_{\rho}^{\prime} = {\frac{n}{z \cdot R_{M}} \cdot \frac{X_{p}}{X_{\vartheta}}}},$wherein n is a molar mass, z a real gas factor of the medium, especiallya real gas factor ascertained according to one of industrial standardsAGA 8, AGA NX-19, SGERG-88 IAWPS-IF97, ISO 12213:2006 and/or withapplication of the temperature measurement signal and/or the pressuremeasurement signal, and R_(M) is the relative gas constant of the mediumto be measured, corresponding with absolute gas constant R/n normalizedwith the molar mass n of the medium, with R=8.3143 J/(K mol).
 36. Themeasuring system as claimed in claim 34, wherein: said measuringelectronics ascertains the provisional density measured-value (X′_(ρ)),at least at times, based on the formula: $\begin{matrix}{X_{\rho}^{\prime} = {\pi_{{IAWPS}\text{-}{IF}\; 97} \cdot \gamma_{{IAWPS}\text{-}{IF}\; 97}}} \\{{= {\frac{X_{p}}{P_{{IAWPS}\text{-}{IF}\; 97}^{*}} \cdot \frac{g_{{IAWPS}\text{-}{IF}\; 97}}{R_{M} \cdot X_{\vartheta}}}},}\end{matrix}$ where π_(IAWPS-IF97)=X_(p)/P*_(IAWPS-IF97) andγ_(IAWPS-IF97)=g_(IAWPS-IF97)/(R_(M)*X_(θ)), wherein P* is amedium-specific, critical pressure according to industrial standardIAWPS-IF97, especially 16.53 MPa for the case wherein the medium to bemeasured is water, above which the medium to be measured, in any case,cannot be liquid, and g_(IAWPS-IF97) is a medium-specific, free enthalpy(Gibbs free energy) according to industrial standard IAWPS-IF97.
 37. Themeasuring system as claimed in claim 34, wherein: said measuringelectronics ascertains, repetitively during operation, a density errorcorresponding with a deviation, especially a relative deviation, betweenthe provisional density measured value (X′_(ρ)) and the densitymeasured-value (X_(ρ)), and wherein, especially, the measuringelectronics outputs such in the form of a numerical density error value.38. The measuring system as claimed in claim 37, wherein: said measuringelectronics outputs the instantaneous density error in the form of anumerical density error value and/or compares the instantaneous densityerror with at least one, predetermined, reference value, and, based onthis comparison, generates, at times, an alarm signaling an undesired,especially impermissibly high, discrepancy between the provisionaldensity measured-value (X′_(ρ)) and the density measured-value (X_(ρ)).39. The measuring system as claimed in claim 34, wherein: said measuringelectronics ascertains the density measured-value (X_(ρ)) withapplication both of the provisional density measured-value (X′_(ρ)) andalso the density correction value (X_(K)), especially based on theformula: X_(ρ)=X′_(ρ)·X_(K).
 40. The measuring system as claimed inclaim 39, wherein: said measuring electronics applies the densitycorrection value (X_(K)) in generating the density measured-value(X_(ρ)), solely when it amounts to at least one, especially lying in arange between 1 and 1.2.
 41. The measuring system as claimed in claim39, wherein: said measuring electronics applies the density correctionvalue (X_(K)) in generating the density measured-value (X_(ρ)), solelywhen it amounts to at most one, lying especially in a range between 0.8and
 1. 42. The measuring system as claimed in claim 34, wherein: thecompensation factor (K) is so selected that it fulfills the followingformula:${K = {\Delta \; X\; {\rho \cdot \frac{X_{\vartheta}}{X_{v}^{2}}}}},$wherein ΔX_(ρ) is a measuring system specific deviation ascertained inadvance, especially in the course of a calibration of the same and/or ofa measuring system of essentially equal type with known reference mediumand/or in the course of startup of the measuring system on-site,especially a calculated and/or measured deviation, which the provisionaldensity measured-value (X′_(ρ)), ascertained for a reference mediumdefined at least as regards its actual density, ρ_(Ref), has from thesame density, ρ_(Ref), of the reference medium.
 43. The measuring systemas claimed in claim 42, wherein: the compensation factor (K) fulfillsthe following formula:$K = {{\Delta \; X\; {\rho \cdot \frac{X_{\vartheta}}{X_{v}^{2}}}} = {\left( {\frac{X_{\rho}^{\prime}}{\rho_{Ref}} - 1} \right) \cdot {\frac{X_{\vartheta}}{X_{v}^{2}}.}}}$44. The measuring system as claimed in claim 1, further comprising: atleast one flow sensor communicating, at least at times, with themeasuring electronics, placed at a flow measuring point, and reactingprimarily to a local flow parameter, especially also to changes of thesame, especially a flow parameter averaged over a cross section of theprocess line, especially a flow velocity, a volume flow or a mass flow,of the medium to be measured, especially a medium which is at leastpartially gaseous, wherein: said flow sensor delivers at least one flowmeasurement signal influenced by the local flow parameter; saidmeasuring electronics, with application at least of the flow measurementsignal, generates a velocity measured signal (X_(v)), especially adigital velocity measured-value, which represents, instantaneously, theflow velocity of the flowing medium, as well as, based on thetemperature measurement signal, additionally a temperaturemeasured-value (X_(θ)), especially a digital temperature measured-value,which represents, instantaneously, a local temperature of the medium,especially the temperature of the medium at the temperature measuringpoint, and wherein the measuring electronics ascertains the densitymeasured-value (X_(ρ)), at least at times, based on the formula:$\begin{matrix}{X_{\rho} = \frac{n \cdot X_{p}}{z \cdot R_{M} \cdot \left( {X_{\vartheta} + {K \cdot X_{v}^{2}}} \right)}} \\{{= {\frac{n \cdot X_{p}}{z \cdot R_{M} \cdot X_{\vartheta}} \cdot \frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}}},}\end{matrix}$ wherein n is a molar mass, z a real gas factor of themedium, especially a real gas factor ascertained according to one ofindustrial standards AGA 8, AGA NX-19, SGERG-88 IAWPS-IF97, ISO12213:2006 and/or with application of the temperature measurement signaland/or the pressure measurement signal, and R_(M) the relative gasconstant of the medium to be measured, corresponding with the absolutegas constant normalized with the molar mass n of the medium, thus R/n,with R equal to 8.3143 J/(K mol).
 45. The measuring system as claimed inclaim 1, further comprising: at least one flow sensor communicating, atleast at times, with the measuring electronics, placed at a flowmeasuring point, and reacting primarily to a local flow parameter,especially also to changes of the same, especially a flow parameteraveraged over a cross section of the process line, especially a flowvelocity, a volume flow or a mass flow of the medium to be measured,especially a medium which is at least partially gaseous, wherein theflow sensor delivers at least one flow measurement signal influenced bythe local flow parameter, wherein: said measuring electronics, withapplication at least of the flow measurement signal, ascertains avelocity measured-value (X_(v)), especially a digital, velocitymeasured-value, which represents, instantaneously, the flow velocity ofthe flowing medium, as well as generates, based on the temperaturemeasurement signal, repetitively, a temperature measured-value (X_(θ)),especially a digital, temperature measured-value, which represents,instantaneously, a local temperature of the medium, especially thetemperature of the medium at the temperature measuring point, and saidmeasuring electronics ascertains the density measured-value (X_(ρ)), atleast at times, based on the formula: $\begin{matrix}{X_{\rho} = {\pi_{{IAWPS}\text{-}{IF}\; 97} \cdot \gamma_{{IAWPS}\text{-}{IF}\; 97} \cdot \frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}}} \\{{= {\frac{X_{\rho}}{P_{{IAWPS}\text{-}{IF}\; 97}^{*}} \cdot \frac{g_{{IAWPS}\text{-}{IF}\; 97}}{R_{M} \cdot X_{\vartheta}} \cdot \frac{1}{\left( {1 + {K \cdot \frac{X_{v}^{2}}{X_{\vartheta}}}} \right)}}},}\end{matrix}$ wherein P* is a medium-specific, critical pressureaccording to industrial standard IAWPS-IF97 for the case in which themedium to be measured is water, above which the medium to be measuredcan, in any case, not be liquid, and g medium-specific, free enthalpy(Gibbs free energy) according to industrial standard IAWPS-IF97.
 46. Themeasuring system as claimed in claim 20, wherein: said measuringelectronics communicates, at least at times, with the flow sensor andwherein the measuring electronics, with application at least of the flowmeasurement signal, ascertains a volume flow measured-value (X_(v)),especially a digital, volume flow measured-value, instantaneouslyrepresenting a volume flow rate of the flowing medium.
 47. The measuringsystem as claimed in claim 46, wherein: said measuring electronics, withapplication at least of the density measured-value and the volume flowmeasured-value ascertains a mass flow measured-value (X_(m)), especiallya digital, mass flow measured-value, representing, instantaneously, amass flow rate of the flowing medium.
 48. The measuring system asclaimed in claim 20, wherein: said measuring electronics, withapplication at least of the temperature measurement signal, the pressuremeasurement signal and the flow measurement signal, ascertains a massflow measured-value, especially a digital, mass flow measured-value,representing, instantaneously, a mass flow rate of the flowing medium.49. The measuring system as claimed in claim 20, wherein: the flowmeasuring point is located upstream of the temperature measuring pointand/or upstream of the pressure measuring point.